\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{jinque} \pdfinfo{ /Title (cs1010s-midterm-cheat-sheet-pg2.pdf) /Creator (Cheatography) /Author (jinque) /Subject (CS1010S Midterm pg2 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}{126EA3} \definecolor{LightBackground}{HTML}{F0F5F9} \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{CS1010S Midterm pg2 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{jinque} via \textcolor{DarkBackground}{\uline{cheatography.com/194546/cs/40594/}}} \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}jinque \\ \uline{cheatography.com/jinque} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 3rd October, 2023.\\ 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*}{2} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{sum(term, a next, b)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{term: fn applied to each term \newline % Row Count 1 (+ 1) term(a): first term \newline % Row Count 2 (+ 1) next: applied b - a times \newline % Row Count 3 (+ 1) b: no. of terms (0 is returned for the (b+1)\textasciicircum{}th\textasciicircum{} term% Row Count 5 (+ 2) } \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}{sum implementation}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{def sum(term, a, next, b): \newline % Row Count 1 (+ 1) sum(a, b) = t(a) + t(n(a)) + t(n\textasciicircum{}2\textasciicircum{}(a)) + ... + t(n\textasciicircum{}(b-a)\textasciicircum{}(a)) + 0 \newline % Row Count 3 (+ 2) if a \textgreater{} b: return 0 \newline % Row Count 4 (+ 1) else: return term(a) + sum(term, next(a), next, b)% Row Count 5 (+ 1) } \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}{fold(op, f, n)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{{\bf{n}}: op applied for {\bf{n times}} \newline % Row Count 1 (+ 1) fold\_right: \newline % Row Count 2 (+ 1) (f(n) ⨁ (f(n -1) ⨁ (f(n-2) … ⨁ (f(1) ⨁ f(0)) \newline % Row Count 4 (+ 2) (4 - (3 - (2 - (1 - 0)))) \newline % Row Count 5 (+ 1) fold\_left: \newline % Row Count 6 (+ 1) (((f(0) ⨁ f(1)) ⨁ f(2)) ⨁ … f(n) → n + 1 times \newline % Row Count 8 (+ 2) Matters for non-associative operations e.g. ( (1 - 2) - 3) - 4)% Row Count 10 (+ 2) } \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}{fold\_right}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{fold(..) = op(f(n), fold(n-1)) \newline % Row Count 1 (+ 1) \# = f(n) ⊕ fold(n-1) \newline % Row Count 2 (+ 1) \# = f(n) ⊕ {[} f(n-1) ⊕ fold(n-2) {]} \newline % Row Count 3 (+ 1) \# = f(n) ⊕ f(n-1) ⊕ fold(n-2) -{}-{}- assumes op is assoc./commu. \newline % Row Count 5 (+ 2) \# = f(n) ⊕ f(n-1) ⊕ f(n-2) ⊕ ... ⊕ f(n-(n-1)) ⊕ fold(n-n) \newline % Row Count 7 (+ 2) \# = f(n) ⊕ f(n-1) ⊕ f(n-2) ⊕ ... ⊕ f(n-(n-1)) ⊕ f(0)% Row Count 9 (+ 2) } \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}{fold\_left}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/jinque_1696311018_Screenshot 2023-10-03 at 1.30.14 PM.png}}} \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}{accumulate(fn, initial, seq)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{\textgreater{}\textgreater{}\textgreater{} accumulate(lambda x, y: x + y, 0, (1, 2, 3, 4, 5)) \newline % Row Count 2 (+ 2) 15 \newline % Row Count 3 (+ 1) \textgreater{}\textgreater{}\textgreater{} accumulate(lambda x, y: (x, y), (), (1, 2, 3, 4, 5)) \newline % Row Count 5 (+ 2) (1, (2, (3, (4, (5, ()))))% Row Count 6 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{seq contains n elements \newline when seq{[}n{]} == () i.e. index out of range, \newline initial is returned} \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}{enumerate\_interval(low, high)}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{enumerate\_interval(2, 7)} \tn \mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}(2, 3, 4, 5, 6, 7)} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{enumerate\_interval(1, 1)} \tn \mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}(1,)} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{enumerate\_interval(4, -1)} \tn \mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}()} \tn % Row Count 6 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{8.4cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{sum and product using fold}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{def sum\_of\_int(a, b): \newline % Row Count 1 (+ 1) return fold(op = lambda x, y: x + y, f = lambda x: a + x, n = b - a) \newline % Row Count 3 (+ 2) \# a + (a + 1) + (a + 2) + ... + b - 1, b \newline % Row Count 4 (+ 1) \# b = a + (b - a) \newline % Row Count 5 (+ 1) def product\_int(a, b): \newline % Row Count 6 (+ 1) return fold(op = lambda x, y: x * y, f = lambda x: a + x, n = b - a)% Row Count 8 (+ 2) } \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}{fold2(op, term, a, next, b, base)}} \tn \SetRowColor{white} \mymulticolumn{1}{x{8.4cm}}{fold2() = term(a) ⨁ {[}term(next(a)) ⨁ {[}.. ⨁ base{]} \newline % Row Count 2 (+ 2) \#op applied for (b-a) times \newline % Row Count 3 (+ 1) \#base occurs when b \textgreater{} a% Row Count 4 (+ 1) } \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}{iterative fold (left)}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{x{8.4cm}}{def iter\_fold(op, f, n): \newline res = f(0) \newline for i in range(n): \newline res = op(res, f(i + 1)) \newline return res} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}