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% Document Info
\author{dmytronoks}
\pdfinfo{
  /Title (algorithms-cs50.pdf)
  /Creator (Cheatography)
  /Author (dmytronoks)
  /Subject (Algorithms (CS50) Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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    {\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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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algorithms (CS50) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{dmytronoks} via \textcolor{DarkBackground}{\uline{cheatography.com/158792/cs/33506/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}dmytronoks \\
  \uline{cheatography.com/dmytronoks} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 5th August, 2022.\\
   Updated 4th August, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Definition}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Algorithm}} is a step-by-step set of instructions for completing a task.% Row Count 2 (+ 2)
} \tn 
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\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Search Algorithms}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Linear Search}}: Iterate across the array from left to right, searching for a specified element. & {\bf{Worst case O(n)}}: the target element is the last element of the array or it doesn't exist at all. {\bf{Best case Ω(1)}}: the target element is the first element of the array. \tn 
% Row Count 9 (+ 9)
% Row 1
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{\bf{Binary Search}}: Divide and conquer, reducing the search area by half each time, trying to find a target number.   First, the array should be sorted. & {\bf{Worst case O(log n)}}: the target element will be found at the end of the last division or it won't be found at all. {\bf{Best case Ω(1)}}: the target element is the mid-point of the full array. \tn 
% Row Count 19 (+ 10)
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\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Sorting Algorithms}}  \tn
% Row 0
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{\bf{Bubble Sort}}: Swapping pairs of two elements: higher valued elements towards the right and the lower valued elements towards the left. & {\bf{Worst case O(n\textasciicircum{}2)}}: the array is in the reversed order. {\bf{Best case Ω(1)}}: the array is already perfectly sorted and we don't need to make any swaps on the first run. &  \tn 
% Row Count 9 (+ 9)
% Row 1
\SetRowColor{white}
{\bf{Selection Sort}}: Find the smallest unsorted element and add it to the end of the sorted list. & {\bf{Worst case O(n\textasciicircum{}2)}}: iterate over each of the {\emph{n}} elements of the array (to find the smallest unsorted element) → it's at the very end of the array and repeat this proces {\emph{n}} times, since only one element gets sorted on each pass. {\bf{Best case Ω(n\textasciicircum{}2)}}: exactly the same! &  \tn 
% Row Count 23 (+ 14)
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{\bf{Merge Sort}}: Sort smaller arrays and then merge them in sorted order. & {\bf{The best and the worst}} cases are the same: {\bf{n log n}}. &  \tn 
% Row Count 28 (+ 5)
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Big O notation}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Big-O notation}} is a simplified analysis of an algorithm's efficiency. It attempts to answer two questions: \newline % Row Count 3 (+ 3)
{\emph{Q1: how much memory is needed?}} \newline % Row Count 4 (+ 1)
{\emph{Q2: how much time does it take to complete?}}% Row Count 5 (+ 1)
} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Recursion}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{A {\bf{recursive function}} is one that, as part of its execution, invokes itself. \newline % Row Count 2 (+ 2)
Every recursive function has two cases that could apply, given any input: \newline % Row Count 4 (+ 2)
- The {\emph{base case}} → terminate the recursive process \newline % Row Count 6 (+ 2)
- The {\emph{recursive case}} → the recursion occurs% Row Count 7 (+ 1)
} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Example of recursion: the factorial function}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{The {\bf{factorial}} is found by multiplying {\emph{n}} by all the whole numbers less than it. \newline % Row Count 2 (+ 2)
{\bf{Example}}:  \newline % Row Count 3 (+ 1)
5! = 5 x 4 x 3 x 2 x 1 = 120 \newline % Row Count 4 (+ 1)
{\bf{In C:}} \newline % Row Count 5 (+ 1)
`int fact(int n)` \newline % Row Count 6 (+ 1)
`\{` \newline % Row Count 7 (+ 1)
	`if (n == 1)` \newline % Row Count 8 (+ 1)
		`return 1;` \newline % Row Count 9 (+ 1)
	`else` \newline % Row Count 10 (+ 1)
		`return n * fact(n-1);` \newline % Row Count 11 (+ 1)
`\}` \newline % Row Count 12 (+ 1)
Scenario A: The function calls itself in the 'else' clause → recursive case \newline % Row Count 14 (+ 2)
Scenario B: The function terminates in the 'if' clause → base case% Row Count 16 (+ 2)
} \tn 
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% That's all folks
\end{multicols*}

\end{document}