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% Document Info
\author{Priyal kumar (pryl)}
\pdfinfo{
  /Title (sorting-algorithms.pdf)
  /Creator (Cheatography)
  /Author (Priyal kumar (pryl))
  /Subject (Sorting algorithms Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Sorting algorithms Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Priyal kumar (pryl)} via \textcolor{DarkBackground}{\uline{cheatography.com/66402/cs/16808/}}}
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\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}Priyal kumar (pryl) \\
  \uline{cheatography.com/pryl} \\
        \uline{\seqsplit{9pryl}.tiddlyhost.com/\#door:door}
  \end{tabulary}
\vfill
\columnbreak
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 27th August, 2018.\\
   Updated 27th August, 2018.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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% www.emerson.emory.edu/services/latex/latex_169.html
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{4.16 cm} x{3.84 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sorting algorithms and Methods}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{ {\emph{Sorting algorithms}} }} & {\emph{ {\bf{Methods}} }} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Bubble sort & Exchanging \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Heapsort & Selection \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Insertion sort & Insertion \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Introsort & Partitioning \& Selection \tn 
% Row Count 7 (+ 2)
% Row 5
\SetRowColor{white}
Merge sort & Merging \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Patience sorting & Insertion \& Selection \tn 
% Row Count 10 (+ 2)
% Row 7
\SetRowColor{white}
Quicksort & Partitioning \tn 
% Row Count 11 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Selection sort & Selection \tn 
% Row Count 12 (+ 1)
% Row 9
\SetRowColor{white}
Timsort & Insertion \& Merging \tn 
% Row Count 13 (+ 1)
% Row 10
\SetRowColor{LightBackground}
Unshuffle sort & Distribution and Merge \tn 
% Row Count 15 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.192 cm} x{2.128 cm} x{2.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Best and Worst Case}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\emph{ {\bf{Algorithms}} }} & {\bf{ {\emph{Best Case}} }} & {\bf{ {\emph{Worst Case}} }} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Bogosort & n & ∞ \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Bubble sort & n & n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Bucket sort (uniform keys) & - & n\textasciicircum{}2\textasciicircum{}k \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Heap sort & n log n & n log n \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
Insertion sort & n & n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Merge sort & n log n & n log n \tn 
% Row Count 9 (+ 1)
% Row 7
\SetRowColor{white}
Quick sort & n log n & n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 10 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Selection sort & n\textasciicircum{}2\textasciicircum{} & n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 11 (+ 1)
% Row 9
\SetRowColor{white}
Shell sort & n log n & n\textasciicircum{}4/3\textasciicircum{} \tn 
% Row Count 12 (+ 1)
% Row 10
\SetRowColor{LightBackground}
Spreadsort & n & n(k/s+d) \tn 
% Row Count 13 (+ 1)
% Row 11
\SetRowColor{white}
Timsort & n & n log n \tn 
% Row Count 14 (+ 1)
% Row 12
\SetRowColor{LightBackground}
Unshuffle sort & n & kn \tn 
% Row Count 15 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Insertion sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{function insertionSortR(array A, int n) \newline      if n\textgreater{}0 \newline         insertionSortR(A,n-1) \newline         x ← A{[}n{]} \newline         j ← n-1 \newline         while j \textgreater{}= 0 and A{[}j{]} \textgreater{} x \newline             A{[}j+1{]} ← A{[}j{]} \newline             j ← j-1 \newline         end while \newline         A{[}j+1{]} ← x \newline      end if \newline  end function} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Merge sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{function merge\_sort(list m) \newline     // Base case. A list of zero or one elements is sorted, by definition. \newline     if length of m ≤ 1 then \newline         return m \newline  \newline     // Recursive case. First, divide the list into equal-sized sublists \newline     // consisting of the first half and second half of the list. \newline     // This assumes lists start at index 0. \newline     var left := empty list \newline     var right := empty list \newline     for each x with index i in m do \newline         if i \textless{} (length of m)/2 then \newline             add x to left \newline         else \newline             add x to right \newline  \newline     // Recursively sort both sublists. \newline     left := merge\_sort(left) \newline     right := merge\_sort(right) \newline  \newline     // Then merge the now-sorted sublists. \newline     return merge(left, right)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Bogosort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{while not isInOrder(deck): \newline     shuffle(deck)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Bucket sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{function bucketSort(array, n) is \newline   buckets ← new array of n empty lists \newline   for i = 0 to (length(array)-1) do \newline     insert array{[}i{]} into buckets{[}msbits(array{[}i{]}, k){]} \newline   for i = 0 to n - 1 do \newline     nextSort(buckets{[}i{]}); \newline   return the concatenation of buckets{[}0{]}, ...., buckets{[}n-1{]}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Resources}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\seqsplit{https://en.wikipedia.org/wiki/Sorting\_algorithm\#Comparison\_of\_algorithms}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\seqsplit{http://bigocheatsheet.com}} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.66 cm} x{2.356 cm} x{2.584 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Sorting algorithm complexities}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\emph{ {\bf{Algorithms}} }} & {\bf{ {\emph{Average Case}} }} & {\bf{ {\emph{Memory complexity}} }} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Bitonic sorter & log\textasciicircum{}2\textasciicircum{} n & n log\textasciicircum{}2\textasciicircum{} n \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Bogosort & n × n! & 1 \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Bubble sort & n\textasciicircum{}2\textasciicircum{} & 1 \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Bucket sort (uniform keys) & n+k & nk \tn 
% Row Count 7 (+ 2)
% Row 5
\SetRowColor{white}
Burstsort & n(k/d) & n(k/d) \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Counting sort & n+r & n+r \tn 
% Row Count 9 (+ 1)
% Row 7
\SetRowColor{white}
Heap sort & n log n & 1 \tn 
% Row Count 10 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Insertion sort & n\textasciicircum{}2\textasciicircum{} & 1 \tn 
% Row Count 11 (+ 1)
% Row 9
\SetRowColor{white}
Introsort & n log n & log n \tn 
% Row Count 12 (+ 1)
% Row 10
\SetRowColor{LightBackground}
LSD Radix Sort & n(k/d) & n+2\textasciicircum{}d\textasciicircum{} \tn 
% Row Count 13 (+ 1)
% Row 11
\SetRowColor{white}
Merge sort & n log n & n \tn 
% Row Count 14 (+ 1)
% Row 12
\SetRowColor{LightBackground}
MSD Radix Sort (in-place) & n(k/d) & 2\textasciicircum{}d\textasciicircum{} \tn 
% Row Count 16 (+ 2)
% Row 13
\SetRowColor{white}
Patience sort & - & n \tn 
% Row Count 17 (+ 1)
% Row 14
\SetRowColor{LightBackground}
Pigeonhole sort & n+2\textasciicircum{}k\textasciicircum{} & 2\textasciicircum{}k\textasciicircum{} \tn 
% Row Count 19 (+ 2)
% Row 15
\SetRowColor{white}
Quicksort & n log n & log n \tn 
% Row Count 20 (+ 1)
% Row 16
\SetRowColor{LightBackground}
Selection sort & n\textasciicircum{}2\textasciicircum{} & 1 \tn 
% Row Count 21 (+ 1)
% Row 17
\SetRowColor{white}
Shell sort & Depends on gap sequence & 1 \tn 
% Row Count 23 (+ 2)
% Row 18
\SetRowColor{LightBackground}
Spaghetti sort & n & n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 24 (+ 1)
% Row 19
\SetRowColor{white}
Spreadsort & n(k/d) & (k/d)2\textasciicircum{}d\textasciicircum{} \tn 
% Row Count 25 (+ 1)
% Row 20
\SetRowColor{LightBackground}
Stooge sort & n\textasciicircum{}(log 3/log1.5)\textasciicircum{} & n \tn 
% Row Count 27 (+ 2)
% Row 21
\SetRowColor{white}
Timsort & n log n & n \tn 
% Row Count 28 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Bubble sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{procedure bubbleSort( A : list of sortable items ) \newline     n = length(A) \newline     repeat \newline         swapped = false \newline         for i = 1 to n-1 inclusive do \newline             if A{[}i-1{]} \textgreater{} A{[}i{]} then \newline                 swap(A{[}i-1{]}, A{[}i{]}) \newline                 swapped = true \newline             end if \newline         end for \newline         n = n - 1 \newline     until not swapped \newline end procedure} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Quicksort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{algorithm quicksort(A, lo, hi) is \newline     if lo \textless{} hi then \newline         p := partition(A, lo, hi) \newline         quicksort(A, lo, p - 1 ) \newline         quicksort(A, p + 1, hi) \newline  \newline algorithm partition(A, lo, hi) is \newline     pivot := A{[}hi{]} \newline     i := lo     \newline     for j := lo to hi - 1 do \newline         if A{[}j{]} \textless{} pivot then \newline             swap A{[}i{]} with A{[}j{]} \newline             i := i + 1 \newline     swap A{[}i{]} with A{[}hi{]} \newline     return i} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Selection sort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{procedure selection sort  \newline    list  : array of items \newline    n     : size of list \newline  \newline    for i = 1 to n - 1 \newline    /{\emph{ set current element as minimum}}/ \newline       min = i     \newline    \newline       /{\emph{ check the element to be minimum }}/ \newline  \newline       for j = i+1 to n  \newline          if list{[}j{]} \textless{} list{[}min{]} then \newline             min = j; \newline          end if \newline       end for \newline  \newline       /{\emph{ swap the minimum element with the current element}}/ \newline       if indexMin != i  then \newline          swap list{[}min{]} and list{[}i{]} \newline       end if \newline    end for \newline 	 \newline end procedure} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}