# Regex

Cheatsheet

My regular expression cheatsheet, focused on the Python engine. A lot of content is heavily based on (and often shamelessly copied from) the amazing RexEgg and Regular-Expressions.info sites.

## Basics

• A regex is a text string that a regex engine uses to find text or positions in a body of text, typically for the purposes of validating, finding, replacing, and splitting.

• To differentiate between the string that makes up the regex and the string that is being searched, the former is often called regex or pattern and the latter string or subject.

• A (lexical) token is a string with an assigned and thus identified meaning (more here). For instance, the token \w in a pattern stands for a word-character, and will be replaced by that when the engine parses the string.

• The Python regex engine (and all other modern engines) is regex-directed: it attempts all possible permutations of the regex at a character position of the subject before moving on to the next character (which can involve lots of backtracking). In contrast, text-directed engines visit each character in the subject text only once. This makes them faster but also less powerful.

• A regex engine is eager: it scans alternatives in the regex from left to right and returns the first possible match – Jane|Janet would return Jane as a match in Janet is tall.

## Characters

• There are four types of characters: literal characters (e.g. a), metacharacters (^), non-printable characters (\n), and shorthand character classes (\w).

• Literal characters simply match themselves: the single literal character a matches the first a in the string, the sequence of literal characters cat the first occurrence of cat.

• Metacharacters are the twelve punctuation characters from the ACSII table that make regex work its magic: $, (, ), *, +, ., ?, [, \, ^, {, |. To match metacharacters as literals, escape them with a backslash, as in 1\+2=3. Exceptions are { and }, which are only treated as metacharacters when part of a quantifier, and ], which only takes on special meaning when part of a character class). • Non-printable characters or formation marks are characters used to tell word processors how text needs to look and do not appear in printed text. • Shorthand character classes are tokens for certain common character classes. Non-printable characters Character Legend \r Carriage return \n Newline \r\n Line-break on Windows \t Tab \f Form-feed Shorthand character classes Character Legend \d Single digit, short for [0-9] \D Complement of \d, short for [^\d] \w Word character, short for [a-zA-Z\_] \W Complement of \w, short for [^\w] \s Whitespace character, short for [\r\n\t\f\v ] \S Complement of \s, short for [^\s] \v Vertical whitespace, short for [\n\f\r] \V Complement of \v ## Character classes • Character classes tell the engine to match one of several characters. • Importantly: [^a-z]u does not mean “u not preceded by a lowercase letter”, but “u preceded by something that isn’t a lowercase letter”. Hence, the pattern doesn’t match a u at the beginning of a string. (In contrast to the ., the negated character class does match invisible line breaks, though, so the above pattern would match the string \nu.) • Within a character class, metacharacters are literals with the exception of ^, -, \ and ] if they are used in places where they have special meaning: ^ at the beginning, - as part of a range, ] at the end, and \ to escape another special character or to form a token (i.e. always), and ] at the end. Hence, this regex matches them all as literals: []\\-^] (for details on how to includ metacharacters indide character classes without escaping them, see relevant section here here]. Character classes examples Regex Match [ab] One of a or b [^ab] Any character that isn’t a or b (incl. newline) [\w\s] One word or whitespace character [A-By-z1-2] One of A, B, y, z, 1, 2 [ -~] Any character in the printable section of the ASCII table Exercises: 1. Match gray and grey in London is grey; New York, gray.. 2. Match any character that is neither a digit nor a (hidden) line break character. 3. What does q[^u] match in Iraq and Iraq is a country? 4. How could we match any q not followed by a u? 5. Search for a literal * or +. 6. Match any number greater than 10 made up of all the same digit (e.g. 222, 33, 5555). 7. In b ab cb, match b either at the beginning of the string or when preceded by an a. 8. What’s the difference between [\D\S] and [^\d\s]? Solutions: 1. \bgr[ae]y\b. Discussion: need global flag on or use findall() in Python to match both words, otherwise I’ll just get the first one. 2. [\D\V]. Discussion: the negated character classs matches hidden line break character by default (unlike the .), so need to explicitly exclude them. 3. Nothing and q . Discussion: the regex means “q followed by something that is not a u”, not “q not followed by a u”, so it requires something to follow the q, and that something to not be a u. That something, which happens to be a whitespace in the second string, is part of the match. 4. q(?!u). 5. [*+]. Discussion: these two characters have no special meaning within a character class, so no need to escape them. 6. (\d)\1+. Discussion: need a capturing group for this ([\d]{2,}, for instance, would match any two digit number). 7. (?:^|a)b. Discussion: [a^]b would not work here, since ^ is matched literally inside a character class, so need a non-group with an alternation. 8. [\D\S] matches a single character present inside the character class, so a character that is either not a digit or not a space, which is every character. [^\d\s] matches a single character that is not present inside the character class, so that is neither a digit nor a space, which is all letters. ## Quantifiers • A quantifier tells the engine to match the immediately preceding character, token, or subexpression (e.g. (a|b)) a certain number of times. Nomenclature: • Greedy quantifiers: the default property of quantifiers to match as many characters as possible and thus return the longest possible match. E.g. \d+ matches 123 (not 1 or 12) against 123. • Docile quantifiers: the property of a greedy quantifier to backtrack and give up characters to try the rest of the pattern to match. This is the property behind the “possible” in the above definition: a greedy quantifier matches as many characters of the quantified token as it can for the overall pattern to match. E.g. .*c will run all the way to the end of the string abc, fail to match the c in the pattern, backtrack and give up the c character matched by dot-star, try again to match c, succeed, and return. • Lazy quantifiers: the property of a quantifier to match as few characters as necessary and thus return the shortest possible match. Quantifiers are made lazy by appending ?. Example: \d+? matches 1 against 123. Lazy quantifiers are expensive: laziness and helpfulness make the engine advance from the beginning to the end of a string character by character, at each step expanding the match by including the next character, advancing and attempting to match the rest of the pattern, fail, backtrack, and repeat until it finds a match or reaches the end of the string. • Helpful quantifiers: the property of a lazy quantifier to backtrack and match additional characters of the quantified token in the attempt to match the rest of the pattern. This is the property behind the “necessary” in the above definition: a lazy quantifier matches as few characters as it can for the overall pattern to match. E.g. a*?b will first match zero as against aab, advance and try to match the b, fail, backtrack and match the first a, advance and try to match the b, fail again, backtrack and match the second a, advance and try to match the b, succeed and return. • Possessive quantifiers: an optional property of a quantifier that prevents it from giving up previously matched characters if the rest of the pattern doesn’t match (i.e. it makes the quantifier non-docile). We can make a quantifier possessive by appending a +. Example: a++ greedily matches as many as as it can and never gives any of them back. Quantifiers and modifiers: Token Legend ? Match zero or once \* Match zero or more + Match once or more {n} Match n times {n,m} Match between n and m times, n defaults to 0, m to infinity ? Make quantifier lazy {quantifier}+ Make quantifier possessive Matches in string a5aa5: Pattern Matches in GLOBAL mode (total: list) a 3: a, a, a a+ 2: a, aa a+? 3: a, a, a a* 5: a, ‘’, aa, ‘’, '' a*? 6: ‘’, ‘’, ‘’, ‘’, ‘’, ‘’, '' a? 6: a, ‘’, a, a, ‘’, '' a?? 6: ‘’, ‘’, ‘’, ‘’, ‘’, '' a{2} 1: aa a{,2} 5: a, ‘’, aa, ‘’, '' a{,2}? 6: ‘’, ‘’, ‘’, ‘’, ‘’, '' a{1,} 2: a, aa The greedy trap In the string {start} Mary {end} had a {start} little lamb {end}, match all tokens that start with {start} and end with {end}. The naive solution is, {start}.*{end}, which will run over the first {end} to match entire string since .* is greedy – this is the greedy trap. Solutions: • Lazy quantifier: {start}.*?{end}. Computationally inefficient as it proceeds character-by-character left to right with successive backtracking. • Negated character class: {start}[^{]*{end}. An example of the contrast principle, but works only if { never appears inside the delimiters. • Tempered greedy token: {start}(?:(?!{end}).)*{end}. Ensures that the . never matches the opening bracket of {end}, thus making sure we don’t run over an end token. This allows the { to occur inside the string. Because it requires a lookahead at east step, it is no more efficient than the lazy quantifier solution in this case, though. • Explicit greedy alternation: {start}(?:[^{]|{(?!end}))*{end}. This is an example of the say what you want principle: we either want to match characters that aren’t an opening brace or an opening brace not followed by end}. This requires a lookahead only in the rare case where we find an opening brace rather than at each step and is thus more efficient than the tempered greedy token or lazy quantifier solutions. We can optimise the pattern in two ways: avoiding exiting the alternation at each step and instead matching entire sequences of non-brace characters, and avoiding backtracking if the {end} token at the end of the pattern fails to match, which will never be useful. We can achieve these optimisations by either using possessive quantifiers {start}(?:[^{]++|{(?!end}))*+{end} (++ is required to avoid an explosive quantifier) or atomic groups {start}(?>(?:(?>[^{]+)|{(?!end}))*){end}. The lazy trap In {start} Mary {end}00A {start} little {lamb {end}01B, match all tokens that start with {start} and end with {end}, followed by a sequence of digits and a b, which are to be included in the match. The naive solution, {start}.*?{end}\d+B doesn’t work, as it runs over the first {end} to match the entire string (why?) – this is the lazy trap. Solutions: • Atomic groups: {start}(?>.*{end}\d+B) prevents the engine from backtracking once B can’t be matched after the first {end}00 and thus prevents the .* to expand further. • Negated character class: {start}[^{]*{end}\d+B works, but with the usual limitation that it requires the assumption that there are no { between the start and end tokens. • Tempered greedy token: {start}(?:(?!{end}).)*{end}\d+B works just as in the greedy trap solution above. • Explicit greedy alternation: {start}(?:[^{]++|{(?!end}))*+{end}\d+B also works just as in the greedy trap solution above. Exercises: 1. What does the quantifier apply to in the following patterns: \w+, carrots?, (a|b)*, \Qab\E+, (?:(?!{end}).)*. 2. What’s the simplest way to match color or colour? 3. Why is <.+?> not an ideal solution? 4. Match digits of length 2, 4, or 6. 5. If the above solution matches 123456, what does \1 contain? 6. Adapt the regex from above so it always captures the full match. 7. Does A+. match AAA? What about A++.? Explain. 8. Write a regex that matches strings of digits that end with an a, such as 123a, with maximal efficiency. 9. Explain, step-by-step, what happens if we try to match aaac with the pattern ^(a+)*b. 10. In {start} Mary {end} had a {start} little lamb {end}, match all tokens that start with {start} and end with {end}, but only if the string doesn’t contain {mid} or {restart}. Solutions: 1. \w, s, (a|b), b, .. 2. colou?r. 3. Because by default, quantifiers are greedy and so .+ matches as many characters as it can, initially racing all the way to the end of the string, then failing to match >, then backtracking once, trying again, succeeding and (eagerly) returning. To only match the opening token, use <[^>]+>. 4. Because it’s computationally expensive. 5. (\d\d){1,3}. 6. 56. Explanation: the backreference always contains the content of the last iteration of the group, so (\d\d){3} captures the same text as \d\d\d\d(\d\d). 7. ((?:\d\d){1,3}). Explanation: wraps the full match in a capturing group and turns the subexpression we don’t want to capture in a non-capturing group. 8. Solution: yes and no. Explanation: the first pattern first greedily matches all three As in the string, then advances in the pattern and fails to match the dot, backtracks and gives up the last matched A, advances again, succeeds in matching the dot with the last A in the string, and returns. The second pattern also fails to match the dot at first, but because it is possesive it doesn’t backtrack and give up the last-matched A and so simply fails. 9. Solution: \d++a. A possessive quantifier improves efficiency because \d and a are mutually exclusive, so there is never a good reason for the engine to give up characters and backtrack as there cannot be an a inside the (greedily) matched sequence of digits. Hence, if the last matched digit isn’t followed by an a we want the engine to fail immediately. This is what the possessive quantifier does. If we know that the regex can only match at the beginning of the string, then prepending the \A anchor improves efficiency by failing when we can’t match the pattern starting from the first digit in the string instead of stepping through all remaining digits, which can’t possibly match. 10. This is an example of an explosive quantifier: a case where the number of combinations the engine attempts to match by successive backtracking increases exponentially in the length of the string. What happens? a+ matches aaa, *, nothing, and the b fails to match against c. The engine backtracks and makes a+ give up the last matched character, so this now matches aa, * can now repeat the previous pattern – remember, it matches the pattern a+, not the match aa – and matches a, but b again fails to match against c. In the next backtrack, the a+ matched by * gives up the last matched character, the third a, so the first a+ still matches aa, the second a+, nothing, and b fails to match. This keeps going. RexEgg has a useful table to show the match of different repetitions of the a+ component: a+ a+ a+ aaa - - aa a - aa - - a aa - a a a a a - a - - - - - 1. {start}(?:(?!{mid})(?!{restart}).)*?{end}. ## Anchors and word boundaries • Anchors assert that the engine’s current position in a string matches a certain position like the beginning or the end, while boundaries make assertions about what can and cannot be matched to the left and the right of the current position. • ^ matches the position just before the first character of the string, so ^a means “position just before start of string followed by a”. Similarly, $ matches position just after the last character in the string, and c$ means “c followed by the position just after the end of the string”. • Multiline mode makes ^ and $ match positions just before first and just after last character of the line rather than the entire string.

• $ subtlety: if the very last character in a line is a line break, $ matches both just before it and at the very end just after it (i.e. \d+$ matches 123 in both 123 and 123\n. This is true regardless of whether multiline mode is turned on. (If there are multiple line breaks at the end, the above behaviour only applies to the final one, so \d+$ would not match 123 in 123\n\n.)

• \z vs \Z: similar to the above point, in most engines \z matches only at the very end of a string (i.e. after the linebreak if there is one), while \Z is the flexible end-of-string anchor that can match before and after the linebreak at the end of a string. In Python, \Z behaves like \z, and \z doesn’t exist.

Character Legend
^ Matches beginning of string or line (in multiline mode)
$ Matches end of string or line (in multiline mode) \A Matches only beginning of string \Z Matches only very end of string (same as \z in most other engines) \b Matches if one side is a word character and the other isn’t \B Matches wherever \b doesn’t Exercises: 1. Match cat a) on its own or at the end of a word (e.g. tombcat), b) on its own or at the beginning of a word (e.g. catwalk), c) only on its own, d) fully surrounded by word characters, e) fully surrounded or at the beginning or the end but not on its own. 2. Match Jane or Janet. 3. Create a boundary that detects the edge between a letter and a non-letter. 4. In the string 0# 1 #2 #3# 4# #5, match digits where each side is either a hash or the edge of the string (i.e. 0, 3, 5). 5. Within the vernacular of RexEgg, explain the difference between an anchor, a boundary, and a delimiter. 6. Implementing ^ manually: write patterns that match a at the beginning of a) the string, b) each line, c) line three and beyond. Solutions: 1. a) cat\b b) \bcat, c) \bcat\b, d) \Bcat\B, e) \Bcat|cat\B. 2. \bJanet?\b or \b(Jane|Janet)\b. 3. (?i)(?<![a-z])(?=[a-z])|(?<=[a-z])(?![a-z]). Discussion: RexEgg uses the following alternative: (?i)(?<=^|[^a-z])(?=[a-z])|(?<=[a-z])(?=$|[^a-z]). The two versions are the same, but I find the first version easier to read. Using negated character classes requires that we explicitly allow for ^ and $, since otherwise the regex engine tries to match a character that isn’t a letter and fails. Using negative lookarounds solves this, since these succeed whenever the engine cannot match a lowercase letter in the specified position in the string, which is also true if there is a beginning or end of line character in that position. 4. Using capturing group: (?:^|#)(\d)(?:$|#). Using lookarounds: (?<=[#^])\d(?=[#$]). Using double negative delimiter: (?<![^#])\d(?![^#]). The lookbehind asserts: “what immediately precedes the current position is not a character that is not a hash”, which, turning the logic around, is equivalent to “either not a character or a hash”. The logic of the lookahead is similar. This is thus a clever way to match either a particular (set of) characters or the edge of a string. (This works for single-line strings only, as in multiline strings, \n characters at the beginning and end are characters that aren’t a hash.) 5. They all make assertions about the current position in the string: anchors assert that what immediately precedes or follows the furrent position is a particular position in the string such as the beginning of the string or the end of the line; boundaries make assertions about that is immediately to the left and the right of the current position such as a non-word character on the left and a word character to the right; and delimiters are similar to bouldaries but only look on one side, asserting, for instance, that what immediately precedes the current position is not a character. These lines are blurry, however. 6. a) (?s)(?<!.)a, b) (?<!.)a, c) (?<\n.*\n)a. Discussion: in a) we need DOTALL mode so that . matches linebreaks to prevent the engine from matching at the beginning of new lines, in b) we want the engine to match at the beginning of new lines and thus omit DOTALL mode, for c) we need the flexible-width lookbehinds from the regex module. ## Alternation • Character classes like [ab] tell the regex engine to match a single character out of several possible characters; alternations like (Jane|Bob), to match a single regex out of several possible regexes. Exercises: 1. What do cat|dog, \bcat|dog\b, and \b(cat|dog)\b match? 2. Find all occurrences of Get, GetValue, Set, SetValue. Solutions: 1. The first matches any occurrences of the strings (e.g. cat in uncategorised or dog in dogmatic), the second matches words that begin with cat and words that end with dog, the third cat and dog on their own. 2. (Get|Set)(Value)? is reasonably concise and easy to read. It works because ? is greedy, which means it attempts to match GetValue before Get, assuring that it never matches Get in GetValue. ## Groups • Grouping part of a regex together can be useful to apply a quantifier to a group of tokens, to restrict alternation to a part of the pattern, and to use backreference. • There are three types of groups: capturing, non-capturing, and atomic. • Capturing groups have three main uses: 1) reuse matches using backreferences, 2) use captured text as replacement text in search and replace, 3) use captured parts in applications. Capturing groups get numbered from left to right, and, if they have a quantifier, return the value of the last captured iteration. • Non-capturing groups allow for avoiding the capturing overhead when grouping is needed but capturing isn’t. • Atomic groups become solid as a block once the engine leaves the group and thus prevent the engine from backtracking into the group even if the rest of the expression fails to match. This can be useful to avoid unwanted backtracking when groups contain quantifiers or alternation. In the former case, we could also use possessive quantifiers. Character Legend (regex) Capturing group \1, ..., \99 Backreferences to capturing groups (?:regex) Non-capturing group (?P<name>regex) Named capturing group in re module (?P=name) Backreference to named capturing group in re (?<name>regex) Named capturing group in regex module \g<name> Backreference to named capturing group in regex (?>regex) Atomic group Exercises: 1. Find magical dates, dates where the two final year digits are identical to the day and month digits (e.g. 2008-08-08). 2. Capture day, month, year in dd-mm-yyyy dates. 3. Name the groups in the above example (use the regex module). 4. Search for magic dates using a named group. 5. What’s the difference between the result returned from (\w+) and (\w)+ when matching the string Hello? 6. Find all patterns of the form sum of digits = reversed sum of digits (e.g. 22 + 333 = 333 + 22). 7. Find all cases of repeated words in Hello world world this was some great greatness, wasn’t wasn’t it?. 8. A typical URL has the form <protocol>://<host>/<path> (e.g. https://www.abc.com/index.html). Write a regex that captures the host and, if available, the path but not the protocol, yet validates that the protocol is either http or https (inspired by this SO post). 9. Write a regex similar to the previous one, but now validate that the host is one of http, https, or s3. 10. In strings containing Bob says: word, group the entire regex but only capture the word Bob says (e.g. in Bob says: hello capture hello. 11. In strings containing tokens of the form upNUMBER or downNUMBER, capture the tokens. 12. Does (?>A|.B)C match against ABC? 13. Does (?>a+)[a-z]c match against aac? Solutions: 1. \d\d(\d\d)-\1-\1. 2. (\d{2})-(\d{2})-(\d{4}). 3. (?<day>\d{2})-(?<month>\d{2})-(?<year>\d{4}). 4. \d\d(?<yy>\d\d)-\g<yy>-\g<yy> 5. (\w+) returns Hello; (\w)+, o. Discussion: a capturing group with a quantifier contains the last matched iteration. 6. (\d+) \+ (\d+) = \2 \+ \1. 7. (\b[\w']++\b) \b\1\b. Discussion: If we don’t use word boundaries we’d also match the ss in was some and great in great greatness, and without allowing for ' we’d miss the repetition of wasn’t. Adding a possessive quantifier avoids unnecessary backtracking, which we never want here, as we always want to capture full words only. 8. https?://([^/\s]+)(\S+)?. Discussion: The \s inside the character class ensures the match doesn’t include characters that follow the url. We could include / in the second capturing group to be explicit that what immediately follows the host starts with a forward slash, but it’s redundant because the first group matches up to a space character or a forward slash and the second group only matches if what follows directly thereafter is not a space, character, which implies that the second group can only return a match if its content starts with a forward slash. 9. (?:https?|s3)://([^/\s]+)(\S+)?. Discussion: remind yourself why we cannot just add an alternation without a non-capturing group. 10. (?:Bob says: (\w+)). Discussion: a contrived use of a capturing group within a non-capturing group. 11. ((?:up|down)\d+). Discussion: an example of capturing the content of a non-capturing group by wrapping it in a capturing group. 12. No, the engine will match A at beginning of the string and then fail to match C. Because the group is atomic, it won’t backtrack into the group to match .B and fail. 13. No. Similarly to above, the engine greedily matches both as, then the character class matches c, and the final c in the regex fails to match. Because the grouped expression is atomic, the engine doesn’t backtrack and give up one of the two matched as. ## Lookarounds • Just like anchors, lookarounds are zero-length assertions that determine whether a match is possible in a given location. The difference to anchors is that lookarounds match characters rather than positions in the string, but then give up the matched strings and simply return whether or not they existed. The last step is what makes them zero-length matches, which means the regex engine stays at the current position in the subject string rather than advancing. • Lookaheads can contain any regex, lookbehinds can’t: they have to be fixed-length expressions (i.e. literalse, character escapes, character classes, or alternations where all alternatives are of equal length, but not quantifiers or backreferences). This is because the regex engine steps back by the length of the lookbehind to evaluate matches, and thus needs to know said length. (Actually, the regex module can handle flexible-width lookbehinds.) • As a result of the above, capturing groups can only be used in lookaheads. To use them, simply wrap the regex in parentheses. • Lookarounds don’t look way into the distance: (?=A) doesn’t mean “there is an A somewhere to the right”, it asserts that what immediately follows is an A. To look into the distance, you have to include “binoculars” such as .* or, if possible, more specific tokens. Lookaround Name What it does (?=foo) Lookahead Asserts that what immediately follows the current position in foo (?<=foo) Lookbehind Asserts that what immediately precedes the current position is foo (?!foo) Negative\nLookahead Asserts that what immediately follows the current position is not foo (?<!foo) Negative\nLookbehind Asserts that what immediately precedes the current position is not foo Practice: • Write \A using a lookaround. Solution if DOTALL mode is on: (?<!.) Solution if DOTALL mode is off: (?<![\D\d]). Discussion: If DOTALL mode is on an . matches every character including linebreaks, the first lookbehind asserts that what precedes the current position is not any character, so the position must be the beginning of the string. [\D\d] matches any character that is a digit or not a digit, which is any character, and thus achieves the same thing if DOTALL mode is off. • Match e if followed either by aa or bb. Solution: e(?=([ab])\1). • What does q(?=u)i match in “quit”? Solution: nothing. The regex tries to match a u and an i at the same position. • Match words that don’t end in s. Solution: \b\w+(?<!s)\b. Explanation: approach matches words and, at the end postition, looks back to check that the character that immediately precedes the current position, which is the last character, is not an “s”. Needs word boundaries to prevent engine from backtracking and match word without final s. • Explain why A(?=5)(?=[a-z]) doesn’t match A5k and write a regex that does. Solution: Because lookarounds stand their ground: they don’t alter the position in the string, so the second lookahead also starts at A and finds a 5 rather than a letter. A(?=5[a-z]) does the job. • Validate that a password meets the following conditions: 1) must have between 6 and 10 word characters, 2) must include at least one lowercase character, 3) must include at least three uppercase characters, 4) must include a digit. Match valid passwords. Solution: 1) \A(?=\w{6,10}\Z), 2) (?=[^a-z]*[a-z]), 3) (?=(?:[^A-Z]*[A-Z]){3}), 4) (?=[\D]*\d), to match: .*. Complete solution: \A(?=\w{6,10}\Z)(?=[^a-z]*[a-z])(?=(?:[^A-Z]*[A-Z]){3})(?=\D*\d).* Discussion: Why can’t we just use [a-z] to check for condition 2? This will find a match if the string contains a lowercase letter, but, naturally, the engine will also move to the position of that matching character, whereas we want to stay at the first character to perform subsequent lookaheads, so we need a match that starts at the first character. • Show two ways how to remove the redundant lookahead in the above solution. Solution 1: \A(?=[^a-z]*[a-z])(?=(?:[^A-Z]*[A-Z]){3})(?=\D*\d)\w{6,10}\Z Solution 2: \A(?=\w{6,10}\Z)(?=[^a-z]*[a-z])(?=(?:[^A-Z]*[A-Z]){3})\D*\d.*\Z Discussion: When using n lookaheads to validate n conditions we can always put the regex from any of the lookaheads at the end and use it to validate a particular pattern and to match the entire string. If the condition doesn’t already match the entire string as in solution 1, we can always add .*\Z. Why do we need the \Z? Because unless we are in dotall mode, . doesn’t match linebreaks and thus gets us to the end of the line rather than the end of the string. To ensure that the pattern works for the entire string, we thus need \Z. • Explain why, to validate the password above, we need the contrast pattern for parts 2-4 of the solution (i.e. why do we need [^a-z]*[a-z] instead of [a-z]? Solution: because the lookahead doesn’t look into the distance but at the character that immediately follows the current position. [a-z] checks whether what immediately follows the current position is a lowercase character. What we want is to check whether, immediately following the current position. • Validation: Match a single word character that is not an A. Do so using 1) character class set operations, 2) a lookahead, 3) a lookbehind. Solutions: 1. [\w--Q], 2) (?!Q)\w, 3) \w(?<!Q). The latter two are the password validation approach from above. • Tempering the scope of a token: Match any character as long as it’s not followed by {end}. Solution: (:(?!{end}).)*. Discussion: each . is tempered by the negative lookahead, which specifies that the dot cannot be the beginning of the string {end}. We have thus a tempered version of .* – making sure it matches anything except a particular pattern, which can be useful if, for instance, we want to match anything up to a certain pattern (see tempered greedy token solution). • Delimiters: Match everything between #start# and #end#. Solution: (?<=#end#).*?(?=#end#). Discussion: we make the dot-start lazy by adding ? to ensure that the engine matched the first end tag that accurs after the start string rather than the last one. • Inserting text at a position: Insert an underscore between words in strings that are in CamelCase. Solution: (?<=[a-z])(?=[A-Z]) finds the positions, string replacement tool does the rest (see here for an example). • Finding overlapping matches: Write a pattern that extracts abc, bc, c from abc. Solution: (?=(\w)) with GLOBAL flag (re.findall() in Python). Discussion: an unanchored lookaround with a capturing group is just what we need here: at each position, the engine looks ahead until \w+ stops matching and captures the string in between, then moves one position forward in the string and repeats. • Compound lookarounds: 1. match a number that is preceded and followed by exactly one underscore. Solution: (?<=(?<!_)_)\d+(?=_(?!_)). Discussion: the compound lookbehind asserts that what precedes the position at the beginning of the number is a position that is not preceded by an underscore but itself contains an underscore. The compound lookahead asserts that what immediately follows the position at the end of the number is a position with an underscore that is not followed by another underscore. • In the string _rabbit _dog _mouse DIC🐱dog:mouse, where the DIC list at the end contains the list of allowed animals, match each _token named after animals in the allowed list. Solution: _(\w+)\b(?=.*:\1\b). Discussion: don’t forget the second word boundary, as without it, we’d also match _dog if only doggie were in the allowed list. It’s not clear to me, though, why I need the first boundary. • In the above string, why does _(?=.*:(\w+)\b)\1\b) only match _mouse? Solution: Two reasons: 1) because * is greedy and, upon finding an underscore in the string, shoots all the way to the end of the string and backtracks only far enough to match the first colon, which is the one before mouse. Second: because the engine doesn’t backtrack into lookarounds. Once the lookaround has evaluated as true of false, a failure to match further down in the regex doesn’t cause the engine to go back into the lookaround and backtrack further. Hence, lookarounds are atomic. ## Flags and inline modifiers • To use flags in Python’s re module, pass the keyword flags=re.FLAGNAME to the method (e.g. re.findall(pattern, string, flags=re.MULTILINE)). Flag (inline modifier) Legend [A]SCII (?a) Make tokens match ASCII rather than Unicode GLOBAL Don’t return after first match (use re.findall()) [I]GNORECASE (?i) Case insensitive matching [M]ULTILINE (?m) Make ^ and$ match end of line (not end of string)
S, DOTALL (?s) Make . match newline (also called single-line)
X, VERBOSE (?x) Allow linebreaks for easier-to-read regexes

## Subroutines and recursive expressions

• The backreference \1 repeats the characters captured by the first capturing group; subroutine (?1), the pattern defined by the first capturing group. This can be very useful to make long expressions shorter.

• There is lots more to subroutines, but for my current use cases, the basics are enough.

• Recursive patterns are related to subroutines in that a soubroutine can call itself recursively. In addition, (?R) tries to match the entire pattern recursively (This description of the steps the engine takes is very useful).

Exercises:

1. Match instances of Harry meets Sally and Sally meets Harry.

2. Match strings of the form ab, aabb*, aaabbb**.

3. Match the same strings as above, but now as part of a larger string that might contain other characters, including aab, which we’d not want to match.

4. Match stand-alone strings of the form bbmmee, bme, bbbmmmeee that might possibly occur as part of a larger string. \b(b(?>(?1)|m)*e)\b

Solutions:

1. (Harry|Sally) meets (?1).

2. a(?R)?b.

3. \b(a(?1)b)\b. Discussion: this requires wrapping a recursively called subroutine in word boundaries. Using (?R) instead of (?1) would only match ab, since the recursion would also try to match repeated word boundaries.

4. \b(b(?>(?1)|m)+e)\b. Discussion: We need to use a subroutine rather than a recursion of the entire pattern for the same reason as in the previous exercise. The real action happens inside the capturing group: (b(?>(?1)|m)+e) represents the generic pattern pattern to match balanced constructs (I use a + instead of a * quantifier on the atomic group, which ensures there is at least one middle element). How does it work? For the string bbmmee, the first b in the pattern matches, so the engine advances and reaches the alternation inside the atomic group, from which the subroutine matches the second b. The engine again moves on to the alternation, which now matches m greedily one or more times, meaning it eats up all the ms in the centre of the pattern. Finally, the engine tries to match the first e and succeeds, which means it has successfully matched the entire recursive call. The engine now goes back to the initial pattern and tries to match the final e, which also succeeds and results in a successful overall match. We use an atomic group to avoid the engine from unnecessary backtracking (e.g. after matching multiple ms but failing to match an e, the engine would release each m and attempt to match e again, which will never succeed).

## Character class set opetations

• The regex module has supports the set operations intersection, union, and subtraction on character classes. (Inner brackets are optional but can help with readability.)
Operation Pattern String Matches
Intersection r'[\W]&&[\S]]' a.k$_8 ['.', ‘$']
Union r'[ab||\d]' a.k$_8 [‘a’, 8] Subtraction r'[\w--k]' a.k$_8 [‘a’, ‘_’, 8]

## Gotchas

Exercises:

1. Why doesn’t [a-z]+ match Cat? How can you fix it?

2. Why doesn’t My .* cat match the below string? How can you fix it?

My dog and my cat

3. How can we avoid the regex cat from matching in the string certificate but find it in patterns like _cat12?

4. The regex [128]|18 is supposed to match 1, 2, 8, and 18. In the string 18 18, (a) what does it match without any flags? (b) what does it match with the global flag on? (c) when would it match 18 and why? (d) how could it be improved to achieve its aim?

5. We use the pattern x* with replacement string y. Running it on x, we get yy, running it on a we get yay. What’s going on?

Solutions:

1. Because regex is case-sensitive by default and thus, as writte, only matches lowercase characters. Could either us an inline modifier (?i)[a-z]+ or explicitly search for uppercase and lowercase characters [A-Za-z]+.

2. Because . does not match line breaks by default. The easiest way to fix this is to use DOTALL mode (also called single-line mode) (?s) My .* cat.

3. If we only ever wanted cat on its own, simple word boundaries \bcat\b would do. To match it when surrounded by non-letter word characters, we need real-word boundaries.

4. (a) 1, (b) [1, 8, 1, 8]. This surprised me for a moment: remember that the engine scans alternatives in the regex left to right, eagerly returns the first match, and then moves on to the next character in the string. (c) Never, since it will always match the 1 and move on without attempting to match the right-hand side of the alternation in the pattern. (d) Depending on the context, we could just reverse the alternation to 18|[128], or, more securely, use anchors or boundaries \b(?:[128]|18)\b.

5. Zero matches! In the first case, x* first matches x at position 0 of the string and replaces it with y, and then matches the empty space at position 1 after the x and replaces it as well. In the second case, the regex matches the empty string at position zero and replaces it, moves past the a to position 1, and again matches and replaces the empty string, giving us yay.

## The elements of regex style

Inspired and heavily based on this fantastic section from the RexEgg page.

To write good regex, say shat you mean. Say it clearly.

A string goes from \A to \Z (in re; to \z, in regex).

• Summary mnemonic: Greedy atoms anchor again.: greedy vs lazy, the cost of greedy and workarounds (say what you want, contrast); should parts be made atomic?; should I use anchors or boundaries?; should I use repeating subpattern syntax?

• To match or to capture? The full match is just another capture, in Python and many other engines referred to as group 0 and, by convention called “the match”. So there is no difference between the two approaches. Best practice advise: use whatever gets the job done, while aiming to reduce overhead by reducing the number of capturing groups (use non-capturing groups if useful).

• To split or to match all? They are a different way of looking at the same approach, so use whichever is easier to get the job done.

• Whenever possible, anchor. It ensures that the engine finds the match in the right place, and often saves unnecessary backtracking.

• Say what you want and don’t want, and avoid “dot-star soup”. It saves unnecessary backgtracking and is clearer to read.

• Create contrast with consequtive tokens that are mutually exclusive (\D and \d, or [^a-z] and [a-z]). It can simplify patterns and save unnecessary backtracking. Example: to find strings with exactly three digits that are located at the end, I might start with ^.+\d{3}$. This doesn’t work because . also matches digits, so I’d match abc12345. I could use negative lookbehind like so: ^.+(?\<!\d), but this would still match ab3c123. The real solution is to use mutually exclusive tokens to start with: ^\D+\d{3}$.

• Beware of lazyness. Avoid lazy quantifiers in favour and use contrast to say what you want to save unnecessary backtracking. Example: {.*?} matches everything inside curly brackets, but backtracking is costly as they backtrack at every step. {[^}]*} is more direct and faster.

• Use greediness and laziness deliberately. A greedy quantifier may shoot all the way to the end of the string, a lazy one tuck along backtracking at every step. Either can be useful when employed for a suitable purpose.

• Use atomic quantifiers. They can save a lot of backtracking.

• Design to fail: Compose regexes to minimise the number of unnecessary unsuccessful attempts. Example: with GLOBAL and MULTILINE modes on, (?=.*flea).* matches lines that contain “flea”. But for lines that don’t contain flea, it unnecessarily tries the lookahead at every single character. Anchoring the lookahead at the start of the line, ^(?=.*flea).*, remedies that by only looking ahead from the first position of each line.

## Frequently used patterns

Work in progress:

• Match all strings inside quotation marks in the below block.

These are ‘string one’ and ‘string two’ and ‘that’s string three’.

Thus far (with global flag/findall()):

• ‘.*’ Doesn’t work because * is greedy and matches ‘string one’ and ' and similar match on second line.
• ‘.*?’ Doesn’t match string two since . doesn’t match line-breaks and get’s mixed up on second line.
• [^'\v]+ Behaves as the above
• [^']+ Now matches second string but including the linebreak, which we don’t want as part of the match, and still gets tripped up by that’s.
• Wanted: match string two but then exclude \v from match, ignore ' that are part of a word.