\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{cheatyboi}
\pdfinfo{
  /Title (alg420.pdf)
  /Creator (Cheatography)
  /Author (cheatyboi)
  /Subject (Alg420 Cheat Sheet)
}

% Lengths and widths
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\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
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% Font and Colours
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\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{Alg420 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{cheatyboi} via \textcolor{DarkBackground}{\uline{cheatography.com/55656/cs/14797/}}}
\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}cheatyboi \\
  \uline{cheatography.com/cheatyboi} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 20th February, 2018.\\
   Updated 20th February, 2018.\\
   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*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sieve of Erath}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{// Java program to print all primes smaller than or equal to \newline // n using Sieve of Eratosthenes \newline   \newline class SieveOfEratosthenes \newline \{ \newline     void sieveOfEratosthenes(int n) \newline     \{ \newline         // Create a boolean array "prime{[}0..n{]}" and initialize \newline         // all entries it as true. A value in prime{[}i{]} will \newline         // finally be false if i is Not a prime, else true. \newline         boolean prime{[}{]} = new boolean{[}n+1{]}; \newline         for(int i=0;i\textless{}n;i++) \newline             prime{[}i{]} = true; \newline           \newline         for(int p = 2; p{\emph{p \textless{}=n; p++) \newline         \{ \newline             // If prime{[}p{]} is not changed, then it is a prime \newline             if(prime{[}p{]} == true) \newline             \{ \newline                 // Update all multiples of p \newline                 for(int i = p}}2; i \textless{}= n; i += p) \newline                     prime{[}i{]} = false; \newline             \} \newline         \} \newline           \newline         // Print all prime numbers \newline         for(int i = 2; i \textless{}= n; i++) \newline         \{ \newline             if(prime{[}i{]} == true) \newline                 System.out.print(i + " "); \newline         \} \newline     \}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.92234 cm} x{1.60195 cm} x{1.05271 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{3 Types of Decrease and Conquer}}  \tn
% Row 0
\SetRowColor{LightBackground}
Decrease by constant & Decrease by constant factor & \seqsplit{variable-Size} decrease \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
insertion sort & binary search and bisection method & Euclid's \seqsplit{algoirthm} \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
topolgical sorting & \seqsplit{exponentiation} by squaring & \seqsplit{selection} by \seqsplit{partition} \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
algorithms for generating permutations, subsets & \seqsplit{multiplication} a la russe & nim-like games \tn 
% Row Count 12 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Summations}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/cheatyboi_1519095354_summations-1.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Complexities}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/cheatyboi_1519075717_big-o.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DFS}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/cheatyboi_1519076312_9fa1119.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{BFS}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/cheatyboi_1519076254_fdec3c2.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.32733 cm} x{1.60195 cm} x{1.64772 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Brute-Force Problems}}  \tn
% Row 0
\SetRowColor{LightBackground}
Problem & Method & Complexity \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
TSP & Exhaustive & N! \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
KnapSack & Exhaustive & n*W \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Topological Sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/cheatyboi_1519093947_topsort.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Order: 5,4,2,3,1,0}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Generate Permutations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Example n=3: \newline % Row Count 1 (+ 1)
start: 1 \newline % Row Count 2 (+ 1)
12, 21 \newline % Row Count 3 (+ 1)
123, 132, 312 \newline % Row Count 4 (+ 1)
321, 231, 213 \newline % Row Count 5 (+ 1)
finish% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Euclidean Algorithm}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Example: \newline % Row Count 1 (+ 1)
GCD(270,192) \newline % Row Count 2 (+ 1)
270/192 = 1 R 78 \newline % Row Count 3 (+ 1)
GCD(192, 78) \newline % Row Count 4 (+ 1)
192/78 = 2 R 36 \newline % Row Count 5 (+ 1)
GCD(78,36) \newline % Row Count 6 (+ 1)
78/36 = 2 R 6 \newline % Row Count 7 (+ 1)
GCD(36/6) \newline % Row Count 8 (+ 1)
36/6 = 6 R0 \newline % Row Count 9 (+ 1)
since R = 0, 6 is GCD% Row Count 10 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.09034 cm} x{2.88666 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Brute Force Pros vs Cons}}  \tn
% Row 0
\SetRowColor{LightBackground}
Pros & Cons \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Wide applicability & Rarely Yields Efficient \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Simple & Unacceptably Slow \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Reasonable Algorithms & Not as constructive as others \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}