\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Ishan324}
\pdfinfo{
  /Title (cmpsc-200-exam-2.pdf)
  /Creator (Cheatography)
  /Author (Ishan324)
  /Subject (CMPSC 200 Exam 2 Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{A3A3A3}
\definecolor{LightBackground}{HTML}{F3F3F3}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{CMPSC 200 Exam 2 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Ishan324} via \textcolor{DarkBackground}{\uline{cheatography.com/20950/cs/3806/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Ishan324 \\
  \uline{cheatography.com/ishan324} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 1st April, 2015.\\
   Updated 12th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Three Categories of Code}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{Sequences}} - lines of code executed one after another \newline % Row Count 2 (+ 2)
{\bf{Selection Structures}} - executes some piece of code if some known condition is true, otherwise executes some alternative. \newline % Row Count 5 (+ 3)
{\bf{Repetition Structures}} - (loops) causes a group of statements to be executed multiple times.% Row Count 7 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Break and Continue}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{Break}} statements cause the termination of the smallest enclosing while or for loop.  \newline % Row Count 2 (+ 2)
{\bf{Continue}} statements skip to the rest of loop, advancing to the next loop pass.% Row Count 4 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Time}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{clock}} gives you the current time \newline % Row Count 1 (+ 1)
{\bf{etime}} compares between a start and end time \newline % Row Count 2 (+ 1)
{\bf{cputime}} returns cpu time since you started matlab \newline % Row Count 4 (+ 2)
{\bf{tic/toc}} works like a stopwatch% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Array vs Matrices}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{Array}} holds stuff: can hold numeric info, char data, or symbolic data. Is "an orderly grouping of information". No special properties by virtue of its existence. \newline % Row Count 4 (+ 4)
{\bf{Matrix}} is a 2D numeric array used in linear algebra. Used extensively in STEM fields and has special properties.% Row Count 7 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{To solve Ax = b}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{Inverse method}} solution = inv(A)*b \newline % Row Count 1 (+ 1)
{\bf{rref command}} A\_augmented  = {[}A b{]} \newline % Row Count 2 (+ 1)
RREF\_result = rref(A\_augmented); \newline % Row Count 3 (+ 1)
solution = RREF\_result(:,end) \newline % Row Count 4 (+ 1)
{\bf{backslash}} solution = A\textbackslash{}b% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Structure Arrays}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{A = 'We Are!' \newline B = {[}1 4; 3 2{]} \newline C = 'Penn State!' \newline D = single({[} 1 2; 3 4{]}) \newline E = \{A, B, C, D\} \%default printing, just shows sizes. \newline celldisp(E) \%needed to generate display \newline  \newline E\{3\} \{\{fa-arrow-right\}\} displays 'Penn State' \newline E\{1\}(1,2) \%1st row, 2nd col of cell 1 w/ multilayer indexing \{\{fa-arrow-right\}\} displays e \newline E\{2\}(:) \%concatenates cell 2 into column vector \newline  \newline N.first = 'Hello'; \newline N.second = 'World'; \newline disp('N is: ') \newline disp(N) \{\{fa-arrow-right\}\} N is: first:'Hello'; second:'World' \newline  \newline orderfields(N) \%orders fields in ASCII dictionary \newline orderfields(N,O) \%orders N field like O is ordered \newline  \newline T = 'myphrase1'; \newline L = rmfield(L,T) \% removes 'myphrase1' field from L} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Short Answer}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{41. {\bf{What is the difference between a matrix and 2D array?}} \newline % Row Count 2 (+ 2)
A matrix is 2D, has special mathematical properties. An array need not be 2D, \newline % Row Count 4 (+ 2)
and has no special mathematical properties, and is merely a "holder" for data. \newline % Row Count 6 (+ 2)
42. {\bf{Why is it a good idea to create a flowchart and pseudocode before you attempt to create a computer program?}} \newline % Row Count 9 (+ 3)
Creating a flowchart and pseduocode before attempting to create a computer \newline % Row Count 11 (+ 2)
program is a good idea because it gives you an opportunity to think your way \newline % Row Count 13 (+ 2)
through the program. A builder wouldn't start building a house without a \newline % Row Count 15 (+ 2)
blueprint; it is advisable to think through your programs as well. \newline % Row Count 17 (+ 2)
43. {\bf{Briefly describe how one would mathematically check if a square matrix is singular. What practical implementation issues arise when implementing that into MATLAB code?}} \newline % Row Count 21 (+ 4)
Mathematically, a matrix is invertible if detA \textasciitilde{}= 0. In terms of \newline % Row Count 23 (+ 2)
implementation, if the determinate is ≈ 0 it can be viewed as effectively singular. \newline % Row Count 25 (+ 2)
You could check the determinant against some sort of tolerance to see if your \newline % Row Count 27 (+ 2)
determinant is close enough to 0 to make your matrix numerically act as singular.% Row Count 29 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{3D array whose values count down}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{nrows = 3;  \newline ncols = 2;  \newline npages = 4;  \newline B = zeros(nrows,ncols,npages); \newline counter = 25; \newline  \newline for k = 1:npages; \newline     for i = 1:nrows; \newline         for j = 1:ncols; \newline             counter = counter - 1; \newline             B(i,j,k) = counter; \newline         end \newline     end \newline end \newline  \newline fprintf('The first page of B is:\textbackslash{}n') \newline disp(B(:,:,1)) \newline etc} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Short Answer}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{44. {\bf{What is the benefit of using cell arrays to store chars instead of using character arrays?}} \newline % Row Count 2 (+ 2)
Character arrays have to have the same number of columns in each row. Cell \newline % Row Count 4 (+ 2)
arrays of chars, however, has no such restriction. \newline % Row Count 6 (+ 2)
45. {\bf{Briefly discuss the difference between cell arrays and structure arrays in MATLAB.}} \newline % Row Count 8 (+ 2)
One of the more prominent differences between cell arrays and structure arrays in \newline % Row Count 10 (+ 2)
MATLAB is content indexing for cells, and the use of fields for structure arrays.% Row Count 12 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}