% use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions.
\documentclass[
	nosolutions
]{../../resources/ormc_handout}


\usepackage{xcolor}
\usepackage{soul}

\definecolor{Light}{gray}{.90}
\sethlcolor{Light}
\newcommand{\htexttt}[1]{\texttt{\hl{#1}}}

\begin{document}

	\maketitle
		{The Regex Warm-Up}
		{Prepared by Mark on \today}

	Yesterday we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is pattern matching, usually in the form of Regular Expressions. \\
	(abbreviated \say{regex}, which is pronounced like \say{gif})

	\vspace{2mm}

	Regex is a language used to specify patterns in a string. You can think it as a concise way to define a DFA, using text instead of a huge graph. \\

	Often enough, a clever regex pattern can do the work of a few hundred lines of code. \\

	\vspace{2mm}

	Like the DFAs we have studied, a regex pattern \textit{accepts} or \textit{rejects} a string. However, we don't usually use this terminology when discussing regex, instead opting to say a pattern \textit{matches} or \textit{doesn't match} a string. \\

	\vspace{5mm}

	\textbf{Quantifiers} \\
	Quantifiers tell us how many of a character to match. \\
	There are four of them:
	\htexttt{+}, \htexttt{*}, \htexttt{?}, and \htexttt{\{ \}}

	\vspace{2mm}

	\htexttt{+} means \say{match one or more of the preceding token} \\
	\htexttt{*} means \say{match zero or more of the preceding token} \\

	For example, the pattern \htexttt{ca+t} will match the following strings:
	\begin{itemize}
		\item \texttt{cat}
		\item \texttt{caat}
		\item \texttt{caaaaaaaat}
	\end{itemize}
	\htexttt{ca+t} will \textbf{not} match the string \texttt{ct}. \\
	The pattern \htexttt{ca*t} will match all the strings above, including \texttt{ct}.
	\vspace{2mm}


	\htexttt{?} means \say{match one or none of the preceeding token} \\
	The pattern \htexttt{linea?r} will match only \texttt{linear} and \texttt{liner} \\
	\vspace{2mm}

	Patterns with brackets \htexttt{\{min, max\}} are the most flexible quantifier. \\
	They specify exactly how many tokens to match: \\
	\htexttt{ab\{2\}a} will match only \texttt{abba}. \\
	\htexttt{ab\{1,3\}a} will match \texttt{aba}, \texttt{abba}, \texttt{abbba}. \\
	\htexttt{ab\{2,\}a} will match any \texttt{ab...ba} with at least two \texttt{b}s.

	\vspace{5mm}

	\problem{}
	Write the patterns \htexttt{a*} and \htexttt{a+} using only \htexttt{\{ \}}.
	\vfill

	\problem{}
	Draw a DFA equivalent to the regex pattern \htexttt{01*0}.
	\vfill

	\pagebreak






	\textbf{Characters, Sets, and Groups}

	Characters tell us what to match.

	Usually we specify them literally, as shown above: \\
	\texttt{a+} means \say{one or more \texttt{a} character} \\

	\vspace{2mm}

	There are, however, other ways we can specify characters. \\

	\vspace{2mm}

	The first such way is the \textit{set}, denoted \htexttt{[ ]}. A set can pretend to be any character inside it. \\
	For example, \htexttt{m[aoy]th} will match \texttt{math}, \texttt{moth}, or \texttt{myth}. \\
	\htexttt{a[01]+b} will match \texttt{a0b}, \texttt{a111b}, \texttt{a1100110b}, and any other similar string. \\

	\vspace{2mm}

	If we want to keep characters together, we can use the \textit{group}, denoted \htexttt{( )}. \\

	Groups work exactly as you'd expect, representing an atomic\footnotemark{} group of characters. \\
	\htexttt{a(01)+b} will match \texttt{a01b} and \texttt{a010101b}, but will \textbf{not} match \texttt{a0b}, \texttt{a1b}, or \texttt{a1100110b}. \\

	\footnotetext{In other words, \say{unbreakable}}


	\problem{}<regex>
	You are now familiar with most of the tools regex has to offer. \\
	Match the following strings:
	\begin{enumerate}
		\item An ISO-8601 date, like \texttt{2022-10-29}. \\
		Invalid dates like \texttt{2022-13-29} should also be matched. \\

		\item A hexadecimal integer of any length.
		\item A UCLA room number, like \texttt{MS 5118} or \texttt{Kinsey 1220B}
		\item Any ISBN-10 of the form \texttt{0-316-00395-7}. \\
		Remember that the check digit can be an \texttt{X}. \\
		Dashes are optional.
	\end{enumerate}



	\vfill





	\problem{}
	If you'd like to know more, check out \texttt{regexr.com}. There's an interative regex prompt that provices explanations, as well as a cheatsheet that explains every regex token there is. You can find a nice set of challenges at \texttt{http://regex.alf.nu} \\
	I especially encourage you to look into this if you are interested in computer science.
	\pagebreak

	\problem{}
	Draw a DFA for each of the following regex strings. \\
	\begin{itemize}
		\item Your solution to \ref{regex}, Part 2
		\item Your solution to \ref{regex}, Part 3
		\item Your solution to \ref{regex}, Part 4
	\end{itemize}
\end{document}