158 lines
5.3 KiB
TeX
158 lines
5.3 KiB
TeX
\documentclass[
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solutions,
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hidewarning,
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\usepackage{xcolor}
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\usepackage{soul}
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\usepackage{hyperref}
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\usepackage[T1]{fontenc} % Fixes texttt braces
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\definecolor{Light}{gray}{.90}
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\sethlcolor{Light}
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\newcommand{\htexttt}[1]{\texttt{\hl{#1}}}
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\title{The Regex Warm-Up}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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Last time, we discussed Deterministic Finite Automata. One interesting application of these mathematical objects is found in computer science: Regular Expressions. \par
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This is often abbreviated \say{regex}, which is pronounced like \say{gif.}
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\vspace{2mm}
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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
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Often enough, a clever regex pattern can do the work of a few hundred lines of code.
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\vspace{2mm}
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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.
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\vspace{5mm}
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Regex strings consist of characters, quantifiers, sets, and groups.
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\vspace{5mm}
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\textbf{Quantifiers} \par
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Quantifiers specify how many of a character to match. \par
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There are four of these: \htexttt{+}, \htexttt{*}, \htexttt{?}, and \htexttt{\{ \}}
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\vspace{2mm}
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\htexttt{+} means \say{match one or more of the preceding token} \par
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\htexttt{*} means \say{match zero or more of the preceding token}
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For example, the pattern \htexttt{ca+t} will match the following strings:
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\begin{itemize}
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\item \texttt{cat}
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\item \texttt{caat}
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\item \texttt{caaaaaaaat}
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\end{itemize}
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\htexttt{ca+t} will \textbf{not} match the string \texttt{ct}. \par
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The pattern \htexttt{ca*t} will match all the strings above, including \texttt{ct}.
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\vspace{2mm}
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\htexttt{?} means \say{match one or none of the preceding token} \par
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The pattern \htexttt{linea?r} will match only \texttt{linear} and \texttt{liner}.
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\vspace{2mm}
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Brackets \htexttt{\{min, max\}} are the most flexible quantifier. \par
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They specify exactly how many tokens to match: \par
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\htexttt{ab\{2\}a} will match only \texttt{abba}. \par
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\htexttt{ab\{1,3\}a} will match only \texttt{aba}, \texttt{abba}, and \texttt{abbba}. \par
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\htexttt{ab\{2,\}a} will match any \texttt{ab...ba} with at least two \texttt{b}s.
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\vspace{5mm}
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\problem{}
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Write the patterns \htexttt{a*} and \htexttt{a+} using only \htexttt{\{ \}}.
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\vfill
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\problem{}
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Draw a DFA equivalent to the regex pattern \htexttt{01*0}.
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\vfill
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\pagebreak
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\textbf{Characters, Sets, and Groups} \par
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In the previous section, we saw how we can specify characters literally: \par
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\texttt{a+} means \say{one or more \texttt{a} character}
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\vspace{2mm}
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There are, of course, other ways we can specify characters.
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\vspace{2mm}
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The first such way is the \textit{set}, denoted \htexttt{[ ]}. A set can pretend to be any character inside it. \par
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For example, \htexttt{m[aoy]th} will match \texttt{math}, \texttt{moth}, or \texttt{myth}. \par
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\htexttt{a[01]+b} will match \texttt{a0b}, \texttt{a111b}, \texttt{a1100110b}, and any other similar string. \par
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You may negate a set with a \htexttt{\textasciicircum}. \par
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\htexttt{[\textasciicircum abc]} will match any character except \texttt{a}, \texttt{b}, or \texttt{c}, including symbols and spaces.
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\vspace{2mm}
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If we want to keep characters together, we can use the \textit{group}, denoted \htexttt{( )}. \par
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Groups work exactly as you'd expect, representing an atomic\footnotemark{} group of characters. \par
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\htexttt{a(01)+b} will match \texttt{a01b} and \texttt{a010101b}, but will \textbf{not} match \texttt{a0b}, \texttt{a1b}, or \texttt{a1100110b}.
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\footnotetext{In other words, \say{unbreakable}}
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\problem{}<regex>
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You are now familiar with most of the tools regex has to offer. \par
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Write patterns that match the following strings:
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\begin{enumerate}[itemsep=1mm]
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\item An ISO-8601 date, like \texttt{2022-10-29}. \par
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\hint{Invalid dates like \texttt{2022-13-29} should also be matched.}
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\item An email address. \par
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\hint{Don't forget about subdomains, like \texttt{math.ucla.edu}.}
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\item A UCLA room number, like \texttt{MS 5118} or \texttt{Kinsey 1220B}.
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\item Any ISBN-10 of the form \texttt{0-316-00395-7}. \par
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\hint{Remember that the check digit may be an \texttt{X}. Dashes are optional.}
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\item A word of even length. \par
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\hint{The set \texttt{[A-z]} contains every english letter, capitalized and lowercase. \\
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\texttt{[a-z]} will only match lowercase letters.}
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\item A word with exactly 3 vowels. \par
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\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.}
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\item A word that has even length and exactly 3 vowels.
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\item A sentence that does not start with a capital letter.
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\end{enumerate}
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\vfill
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\problem{}
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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
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You will find a nice set of challenges at \url{https://alf.nu/RegexGolf}.
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I especially encourage you to look into this if you are interested in computer science.
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\end{document} |