\documentclass[
	solutions,
	hidewarning,
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}


\usepackage{xcolor}
\usepackage{soul}
\usepackage{hyperref}

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


\title{The Regex Warm-Up}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today}

\begin{document}

	\maketitle


	Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \par
	This is often 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 of it as a concise way to define a DFA, using text instead of a huge graph. \par

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

	\vspace{2mm}

	Like the DFAs we've studied, a regex pattern \textit{accepts} or \textit{rejects} a string. However, we don't usually use this terminology with regex, and instead say that a string \textit{matches} or \textit{doesn't match} a pattern.

	\vspace{5mm}

	Regex strings consist of characters, quantifiers, sets, and groups.

	\vspace{5mm}

	\textbf{Quantifiers} \par
	Quantifiers specify how many of a character to match. \par
	There are four of these: \htexttt{+}, \htexttt{*}, \htexttt{?}, and \htexttt{\{ \}}

	\vspace{2mm}

	\htexttt{+} means \say{match one or more of the preceding token} \par
	\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}. \par
	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 preceding token} \par
	The pattern \htexttt{linea?r} will match only \texttt{linear} and \texttt{liner}.
	\vspace{2mm}

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

	\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} \par
	In the previous section, we saw how we can specify characters literally: \par
	\texttt{a+} means \say{one or more \texttt{a} character}

	\vspace{2mm}

	There are, of course, 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. \par
	For example, \htexttt{m[aoy]th} will match \texttt{math}, \texttt{moth}, or \texttt{myth}. \par
	\htexttt{a[01]+b} will match \texttt{a0b}, \texttt{a111b}, \texttt{a1100110b}, and any other similar string. \par
	You may negate a set with a \htexttt{\textasciicircum}. \par
	\htexttt{[\textasciicircum abc]} will match any character except \texttt{a}, \texttt{b}, or \texttt{c}, including symbols and spaces.

	\vspace{2mm}

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

	Groups work exactly as you'd expect, representing an atomic\footnotemark{} group of characters. \par
	\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. \par
	Write patterns that match the following strings:
	\begin{enumerate}[itemsep=1mm]
		\item An ISO-8601 date, like \texttt{2022-10-29}. \par
		\hint{Invalid dates like \texttt{2022-13-29} should also be matched.}

		\item An email address. \par
		\hint{Don't forget about subdomains, like \texttt{math.ucla.edu}.}

		\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}. \par
		\hint{Remember that the check digit may be an \texttt{X}. Dashes are optional.}

		\item A word of even length. \par
		\hint{The set \texttt{[A-z]} contains every english letter, capitalized and lowercase. \\
		\texttt{[a-z]} will only match lowercase letters.}

		\item A word with exactly 3 vowels. \par
		\hint{The special token \texttt{\textbackslash w} will match any word character. It is equivalent to \texttt{[A-z0-9\_]} \\ \texttt{\_} stands for a literal underscore.}

		\item A word that has even length and exactly 3 vowels.

		\item A sentence that does not start with a capital letter.
	\end{enumerate}

	\vfill

	\problem{}
	If you'd like to know more, check out \url{https://regexr.com}. It offers an interactive regex prompt, as well as a cheatsheet that explains every other regex token there is. \par
	You will find a nice set of challenges at \url{https://alf.nu/RegexGolf}.
	I especially encourage you to look into this if you are interested in computer science.
\end{document}