\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{noxlock}
\pdfinfo{
  /Title (hopefullygood.pdf)
  /Creator (Cheatography)
  /Author (noxlock)
  /Subject (hopefullygood 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{hopefullygood Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{noxlock} via \textcolor{DarkBackground}{\uline{cheatography.com/97687/cs/20913/}}}
\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}noxlock \\
  \uline{cheatography.com/noxlock} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 25th October, 2019.\\
   Updated 25th October, 2019.\\
   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}{Bases}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{0x0F \textgreater{} 0000 1111 \newline % Row Count 1 (+ 1)
Convert by each byte for bitstrings. \newline % Row Count 2 (+ 1)
1100 + 11 = \newline % Row Count 3 (+ 1)
1100 + 0011 \newline % Row Count 4 (+ 1)
Pad from the left. \newline % Row Count 5 (+ 1)
0x0F + 0x0A \newline % Row Count 6 (+ 1)
15 + 10 = 25 \newline % Row Count 7 (+ 1)
REMEMBER TO CONVERT BASES BACK UNLESS STATED OTHERWISE% Row Count 9 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{p{0.33363 cm} x{2.36574 cm} p{0.33363 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{3.833cm}}{\bf\textcolor{white}{Logic}}  \tn
% Row 0
\SetRowColor{LightBackground}
p & implies & q \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
0 & 0 & 1 \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
0 & 1 & 1 \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
1 & 0 & 0 \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
1 & 1 & 1 \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{3}{x{3.833cm}}{} \tn 
% Row Count 5 (+ 0)
% Row 6
\SetRowColor{LightBackground}
p & or & q \tn 
% Row Count 6 (+ 1)
% Row 7
\SetRowColor{white}
0 & 0 & 0 \tn 
% Row Count 7 (+ 1)
% Row 8
\SetRowColor{LightBackground}
0 & 1 & 1 \tn 
% Row Count 8 (+ 1)
% Row 9
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1 & 0 & 1 \tn 
% Row Count 9 (+ 1)
% Row 10
\SetRowColor{LightBackground}
1 & 1 & 1 \tn 
% Row Count 10 (+ 1)
% Row 11
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\mymulticolumn{3}{x{3.833cm}}{} \tn 
% Row Count 10 (+ 0)
% Row 12
\SetRowColor{LightBackground}
p & and & q \tn 
% Row Count 11 (+ 1)
% Row 13
\SetRowColor{white}
0 & 0 & 0 \tn 
% Row Count 12 (+ 1)
% Row 14
\SetRowColor{LightBackground}
0 & 1 & 0 \tn 
% Row Count 13 (+ 1)
% Row 15
\SetRowColor{white}
1 & 0 & 0 \tn 
% Row Count 14 (+ 1)
% Row 16
\SetRowColor{LightBackground}
1 & 1 & 1 \tn 
% Row Count 15 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Sets}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Sets have no duplicates, and are unordered. \newline % Row Count 1 (+ 1)
set('john, stop') \newline % Row Count 2 (+ 1)
= \{'j', 'o', 'h', 'n', ',' '', 's', 't', 'o', 'p'\} \newline % Row Count 4 (+ 2)
commas and spaces count as characters \newline % Row Count 5 (+ 1)
A = \{j, o, h, n\}, B = \{s, t, o , p\} \newline % Row Count 6 (+ 1)
A ⋃ B = \{j, o, h, n, s, t , o, p\} \newline % Row Count 7 (+ 1)
A ⋂ B = \{o\} \newline % Row Count 8 (+ 1)
A - B = \{j, h, n\} \newline % Row Count 9 (+ 1)
Symdiff = A ⋃ B - A ⋂ B = \newline % Row Count 10 (+ 1)
\{j, h, n, s, t, p\} \newline % Row Count 11 (+ 1)
= XOR% Row Count 12 (+ 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}{Graphs}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{For (v, w) ∈ E =\textgreater{} (w, v) ∈ E to be true... \newline % Row Count 1 (+ 1)
It must be an undirected graph. \newline % Row Count 2 (+ 1)
(v,w) is an edge in the set of all edges E \newline % Row Count 3 (+ 1)
Trees are graphs but cannot have cycles. \newline % Row Count 4 (+ 1)
Edge list: (NODE, COST, NODE)% 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}{Big O}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Most Efficient \newline % Row Count 1 (+ 1)
O(1) \newline % Row Count 2 (+ 1)
O(logn) \newline % Row Count 3 (+ 1)
O(n) \newline % Row Count 4 (+ 1)
O(nlogn) \newline % Row Count 5 (+ 1)
O(n\textasciicircum{}2) \newline % Row Count 6 (+ 1)
O(n!) \newline % Row Count 7 (+ 1)
Least Efficient \newline % Row Count 8 (+ 1)
logn is hopping halfway between% Row Count 9 (+ 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}{Functions}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Domain = Source/Left \newline % Row Count 1 (+ 1)
Range = Result/Right \newline % Row Count 2 (+ 1)
A relation can be thought of as a set that contains every pair which maps from \newline % Row Count 4 (+ 2)
an element in the domain to an element in the range. \newline % Row Count 6 (+ 2)
For a function, every element in the range is mapped to from a \newline % Row Count 8 (+ 2)
unique element in the domain. This is to say, that an element on the left of this diagram can ONLY map to ONE \newline % Row Count 11 (+ 3)
element on the right.% Row Count 12 (+ 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}{Matrices}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{1 x 2   2 x 1 \newline % Row Count 1 (+ 1)
{[}5, 7{]}   {[}3{]} \newline % Row Count 2 (+ 1)
⠀⠀⠀{[}4{]} \newline % Row Count 3 (+ 1)
If the two inside numbers are the same, dot product can be performed, the resulting matrix is the rows x column% Row Count 6 (+ 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}{Relations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Domain/Range is the same \newline % Row Count 1 (+ 1)
RELATIONS CAN MAP MULTIPLE DOMAIN ELEMENTS TO A RANGE ELEMENT \newline % Row Count 3 (+ 2)
Transitive \newline % Row Count 4 (+ 1)
Triangle line. \newline % Row Count 5 (+ 1)
I'm taller than Pramod, who is taller than Alex, therefore, I'm taller than Alex. \newline % Row Count 7 (+ 2)
x\textgreater{}y, y\textgreater{}z =\textgreater{} x\textgreater{}z \newline % Row Count 8 (+ 1)
Reflexive \newline % Row Count 9 (+ 1)
Diagonal line \newline % Row Count 10 (+ 1)
I know myself \newline % Row Count 11 (+ 1)
x=x \newline % Row Count 12 (+ 1)
Symmetric \newline % Row Count 13 (+ 1)
Diagonal with identical results mirrored. \newline % Row Count 14 (+ 1)
They're sitting across from me, therefore I'm sitting across from them. \newline % Row Count 16 (+ 2)
x+y /2 = y =\textgreater{} x=y% Row Count 17 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}