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The forward tracking quantifier modifier

Published 2012-01-16 C# , Howto , Java , Programming , Python , Regex , Regexp , Regular Expressions , Ruby , Scala , Technology Leave a Comment
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Because of backtracking, we might sometimes match more than we hoped for. The task below is to catch all the div tags in an HTML document and put them in a vector. Our naïve solution gives the wrong answer:

  • '<div>a</div><span>c</span><div>b</div>'.scan /<div>.*<\/div>/ #=> ["<div>a</div><span>c</span><div>b</div>"]

Quantifiers are greedy in regex. They devour as much as they can. The dot in the idiom .* matches anything except newline (remember Barbapapa?). And the asterisk means that this anything is repeated as many times as possible. Since the string ends with a “</div>” the entire substring “a</div><span>c</span><div>b” will be consumed by .*.

There are many stories about greedy people who claim more than they need. As Louis Blanc wrote already 1840 in The Organization of Work: "From each according to his abilities, to each according to his needs." We don't think that the asterisk and the dot in the above example needs to consume more than the substring "<div>a</div>". Alexander Pushkin describes in The Tale of the Fisherman and the Fish how a magic fish promises to fulfill any of the fisherman's whishes. The fisherman's wife starts asking the fish for bigger and better things -- and she gets them -- until she eventually wants to become Ruler of the Sea. Then the magic fish takes back everything he gave the fisherman's wife.

As a complement to backtracking, regex also provides forward tracking. The quantifier tries to take as little as it can and then holds to see if the whole expression can be matched. If the entire expression can't be matched, then the quantifier will capture one more letter and holds to see if it's now possible to match everything. The method is repeated until either we can match everything or we can confirm that there's no possible way to create a match. Does it matter if we use forward tracking instead of backtracking? Well, the strings that can be matched with backtracking can also be matched with forward tracking and vice versa. But, when there are multiple possible matches, forward tracking will sometimes choose a different match than backtracking does.

There is no special symbol for forward tracking quantifiers. Instead, there's modifier symbol -- written as a question mark -- that can be used right after any quantifier. While * means repeat as many times as possible, *? means repeat as few times as possible. Similarly, we can modify all the other quantifiers:

  • At least one, as few as possible: +?
  • Zero or one, preferably zero: ??
  • Between 3 and 5, as few as possible: {3.5}?

Note that the question mark that modifies quantifiers isn't the same question mark that's used as the conditional quantifier. They can even be used in conjunction, as ?? shows above.

Here are some examples. The first one is the solution to the div tag problem:

  • '<div>a</div><span>c</span><div>b</div>'.scan /<div>.*?<\/div>/ #=> ["<div>a</div>", "<div>b</div>"]
  • 'aa'[/a?/] #=> "a"
  • 'aa'[/a??/] #=> ""
  • 'aaaaa'[/a{2,4}/] #=> "aaaa"
  • 'aaaaa'[/a{2,4}?/] #=> "aa"
  • 'aaaaa'[/a{2,}/] #=> "aaaaa"
  • 'aaaaa'[/a{2,}?/] #=> "aa"
  • 'aaaaa'[/a{,4}/] #=> "aaaa"
  • 'aaaaa'[/a{,4}?/] #=> ""

Pomodoro Technique Illustrated -- New book from The Pragmatic Programmers, LLC

Regex memorizing — here’s the pushdown automaton

Published 2011-06-20 finite automata , Howto , Programming , Pushdown Automata , Regex , Regexp , Regular Expressions Leave a Comment
Pushdown automaton that matches all strings with the same number of white and blue dots.

Pushdown automaton that matches all strings with
the same number of white and blue dots.

Formal regular expressions can be described by a finite automaton, but modern regex engines support un-regular operators. The problem with finite automata is that they don’t have any memory. Once they are in a state, they have no idea, how they got there. Wise guys invented the stack. When we add a stack to a finite automaton it becomes very powerful, but also quite complex. And of course, it’s not a finite automaton anymore – it’s a pushdown automaton. Why do I then describe the regex engines as finite automata when pushdown automata is a superset of finite automata?

The finite automaton reads a tape serially. Every new symbol read from the tape, initiates a transition in the automaton from the current state to a new state (the new state may be the same state as the current state). If we are in an accept state when we have read all the tape, then we have a match. In pushdown automata, we add a stack. For every iteration, the pushdown automaton may read a symbol from the tape, pop a symbol from the stack, or both. Depending on the current state, the symbol read from the tape and/or the symbol popped from the stack, the pushdown automaton can now initiate a state transition, push a symbol to the stack, or both. If we end up in a accept state when all the tape is read and the stack is at that time empty then we have a match.

The figure above shows a pushdown automaton that matches any input with the same number of blue and white dots – something that is impossible to describe with a finite automaton. This automaton has two states: a start state and an accept state. The four icons in the middle represents that a dot is popped or pushed from the stack. Suppose that the input is blue-white-white-blue:

  1. Read blue dot and make a transition from the start state, through the third stack icon from the top – i.e. a blue dot is pushed to the stack – and back to the start state.
  2. Read white dot and make a transition from the start state, through the first stack icon – i.e. a blue dot is popped from the stack – and back to the start state. Now the stack is empty.
  3. Read white dot and make a transition from the start state, through the second stack icon from the top – i.e. a white dot is pushed to the stack – and back to the start state.
  4. Read blue dot and make a transition from the start state, through the fourth stack icon – i.e. a white dot is popped from the stack – and to the accept state. Now the stack is empty again and all the input is read. It’s a match.

You can probably feel that the pushdown automaton gives us a tool for all kind of recursive implementations. Now that you understand how, I’ll go back to finite automata in all explanations where possible. It’s important for you to understand e.g. what backtracking and greediness does to performance and what input that will be matched. You don’t need a complicated pushdown automaton to learn that. We’ll stick to finite automaton in this book and at the same time remember that many operators in modern regex engines rely on a stack.

By the way: Did you notice the corner case bug in the pushdown automaton above? Doesn’t an empty input string have the same number of blue and white dots?

Complicated logic calls for regex

Published 2011-05-30 Howto , Java , Programming , Regex , Regexp , Regular Expressions 1 Comment
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When is regex the proper tool? One use case is when you try to verify a text, and the verification rules have complicated logic. I found the following Java method in real production code. It verifies that a time zone designator adheres to the ISO 8601 standard:

public boolean isTimeDesignator(String designator) {
  if (designator.equals("Z")) {
    return true;
  } else if (designator.startsWith(" ") && designator.trim().equals("UTC")) {
    return true;
  } else if (designator.startsWith("+") || designator.startsWith("-")) {
    try {
      int hour = Integer.parseInt(designator.substring(1,3));
      int minute;
      if (3 == designator.length()) {
        minute = 0;
      } else if (5 == designator.length()) {
        minute = Integer.parseInt(designator.substring(3,5));
      } else if (6 == designator.length() && ':' == designator.charAt(3)) {
        minute = Integer.parseInt(designator.substring(4,6));
      } else {
        return false;
      }
      return 0 <= hour && 24 >= hour && 0 <= minute && 59 >= minute;
    } catch (NumberFormatException e) {
      return false;
    }
  }
    
  return false;
}

Only counting the if and else, there are 7 ways the control flow can traverse this code. Adding the NumberFormatException there’s another 3. These ten routes need to be covered by tests.

In ISO 8601, global time is always represented as an offset to Coordinated Universal Time, abbreviated UTC. UTC is informally equivalent to the Greenwich Mean Time, also known as GMT. The designator is an offset in hours and minutes to UTC. Hours are mandatory, but minutes and a colon in-between minutes and hours are optional. Offset zero can be represented as a space and then ‘UCT’ or as ‘Z’. Complicated?

In regex — still in Java — it’s rather crisp to verify:

public boolean isTimeDesignator(String designator) {
  return designator.matches("Z| +UTC|[+-]([01]\\d|2[0-4])(:?[0-5]\\d)?");
}

The latter solution may seem cryptic, for people without experience in regex. But if you think about it, the first solution is cryptic for anyone not proficient in imperative coding. And if you ask me, the first solution is hard to follow for anybody. To understand a regex, you need to understand regex. That’s a tautology. With regex in your repertoire, some problem classes can be solved much more smoothly and the solutions are easier to maintain.

Regex syntax and semantics varies

Published 2011-05-4 Howto , Java , Programming , Regex , Regexp , Regular Expressions , Ruby , Technology 1 Comment

Regex engines do differ in syntax and semantics. This is one reason why you can’t just find an expression with Google and use it in your code – without fully understand it.

Try for example the following in JIRB, the interactive JRuby tool:

irb(main):001:0> require 'java'
=> true
irb(main):002:0> java.util.regex.Pattern.compile("a$").matcher("a\nb").find
=> false
irb(main):003:0> "a\nb"[/a$/]
=> "a"

What happened?

The regex /a$/ matches the letter a just before something checked by a dollar sign assertion. The assert criteria is, by default, not the same in Ruby and Java. In Java, by default, the dollar sign matches at the end of the whole text and before any final line breaks. In Ruby, the dollar sign match at the end of every single line.

Here’s what the three lines of code above means:

  1. First, we need to include the Java libraries by writing require 'java'. This might not be necessary, depending on your setup.
  2. We compile a Java regex and test if part of the string of ‘a’ and ‘b’ with newline in-between can be matched. It can’t.
  3. We compile the same regex in Ruby and test if part of the string of ‘a’ and ‘b’ with newline in-between can be matched. It can.

This is just one of many examples. If you are going to use regexes in your program, you need to understand them. It’s as simple as that.

Pomodoro Technique Illustrated -- New book from The Pragmatic Programmers, LLC

Regex slides

Published 2011-03-21 Howto , Programming , Regex , Regexp , Regular Expressions , Technology 2 Comments
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Slides from my regex session at Turku Agile Day are now available below and at Slideshare:

If you can’t see the whole picture due to Slideshare’s embed limits, click ‘zoom’ -> ‘zoom to page’ in the Slideshare tool bar above.

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