perlretut.pod

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One might initially guess that Perl would find the C<at> in C<cat> and
stop there, but that wouldn't give the longest possible string to the
first quantifier C<.*>.  Instead, the first quantifier C<.*> grabs as
much of the string as possible while still having the regexp match.  In
this example, that means having the C<at> sequence with the final C<at>
in the string.  The other important principle illustrated here is that
when there are two or more elements in a regexp, the I<leftmost>
quantifier, if there is one, gets to grab as much the string as
possible, leaving the rest of the regexp to fight over scraps.  Thus in
our example, the first quantifier C<.*> grabs most of the string, while
the second quantifier C<.*> gets the empty string.   Quantifiers that
grab as much of the string as possible are called I<maximal match> or
I<greedy> quantifiers.

When a regexp can match a string in several different ways, we can use
the principles above to predict which way the regexp will match:

=over 4

=item *

Principle 0: Taken as a whole, any regexp will be matched at the
earliest possible position in the string.

=item *

Principle 1: In an alternation C<a|b|c...>, the leftmost alternative
that allows a match for the whole regexp will be the one used.

=item *

Principle 2: The maximal matching quantifiers C<?>, C<*>, C<+> and
C<{n,m}> will in general match as much of the string as possible while
still allowing the whole regexp to match.

=item *

Principle 3: If there are two or more elements in a regexp, the
leftmost greedy quantifier, if any, will match as much of the string
as possible while still allowing the whole regexp to match.  The next
leftmost greedy quantifier, if any, will try to match as much of the
string remaining available to it as possible, while still allowing the
whole regexp to match.  And so on, until all the regexp elements are
satisfied.

=back

As we have seen above, Principle 0 overrides the others -- the regexp
will be matched as early as possible, with the other principles
determining how the regexp matches at that earliest character
position.

Here is an example of these principles in action:

    $x = "The programming republic of Perl";
    $x =~ /^(.+)(e|r)(.*)$/;  # matches,
                              # $1 = 'The programming republic of Pe'
                              # $2 = 'r'
                              # $3 = 'l'

This regexp matches at the earliest string position, C<'T'>.  One
might think that C<e>, being leftmost in the alternation, would be
matched, but C<r> produces the longest string in the first quantifier.

    $x =~ /(m{1,2})(.*)$/;  # matches,
                            # $1 = 'mm'
                            # $2 = 'ing republic of Perl'

Here, The earliest possible match is at the first C<'m'> in
C<programming>. C<m{1,2}> is the first quantifier, so it gets to match
a maximal C<mm>.

    $x =~ /.*(m{1,2})(.*)$/;  # matches,
                              # $1 = 'm'
                              # $2 = 'ing republic of Perl'

Here, the regexp matches at the start of the string. The first
quantifier C<.*> grabs as much as possible, leaving just a single
C<'m'> for the second quantifier C<m{1,2}>.

    $x =~ /(.?)(m{1,2})(.*)$/;  # matches,
                                # $1 = 'a'
                                # $2 = 'mm'
                                # $3 = 'ing republic of Perl'

Here, C<.?> eats its maximal one character at the earliest possible
position in the string, C<'a'> in C<programming>, leaving C<m{1,2}>
the opportunity to match both C<m>'s. Finally,

    "aXXXb" =~ /(X*)/; # matches with $1 = ''

because it can match zero copies of C<'X'> at the beginning of the
string.  If you definitely want to match at least one C<'X'>, use
C<X+>, not C<X*>.

Sometimes greed is not good.  At times, we would like quantifiers to
match a I<minimal> piece of string, rather than a maximal piece.  For
this purpose, Larry Wall created the I<minimal match> or
I<non-greedy> quantifiers C<??>, C<*?>, C<+?>, and C<{}?>.  These are
the usual quantifiers with a C<?> appended to them.  They have the
following meanings:

=over 4

=item *

C<a??> means: match 'a' 0 or 1 times. Try 0 first, then 1.

=item *

C<a*?> means: match 'a' 0 or more times, i.e., any number of times,
but as few times as possible

=item *

C<a+?> means: match 'a' 1 or more times, i.e., at least once, but
as few times as possible

=item *

C<a{n,m}?> means: match at least C<n> times, not more than C<m>
times, as few times as possible

=item *

C<a{n,}?> means: match at least C<n> times, but as few times as
possible

=item *

C<a{n}?> means: match exactly C<n> times.  Because we match exactly
C<n> times, C<a{n}?> is equivalent to C<a{n}> and is just there for
notational consistency.

=back

Let's look at the example above, but with minimal quantifiers:

    $x = "The programming republic of Perl";
    $x =~ /^(.+?)(e|r)(.*)$/; # matches,
                              # $1 = 'Th'
                              # $2 = 'e'
                              # $3 = ' programming republic of Perl'

The minimal string that will allow both the start of the string C<^>
and the alternation to match is C<Th>, with the alternation C<e|r>
matching C<e>.  The second quantifier C<.*> is free to gobble up the
rest of the string.

    $x =~ /(m{1,2}?)(.*?)$/;  # matches,
                              # $1 = 'm'
                              # $2 = 'ming republic of Perl'

The first string position that this regexp can match is at the first
C<'m'> in C<programming>. At this position, the minimal C<m{1,2}?>
matches just one C<'m'>.  Although the second quantifier C<.*?> would
prefer to match no characters, it is constrained by the end-of-string
anchor C<$> to match the rest of the string.

    $x =~ /(.*?)(m{1,2}?)(.*)$/;  # matches,
                                  # $1 = 'The progra'
                                  # $2 = 'm'
                                  # $3 = 'ming republic of Perl'

In this regexp, you might expect the first minimal quantifier C<.*?>
to match the empty string, because it is not constrained by a C<^>
anchor to match the beginning of the word.  Principle 0 applies here,
however.  Because it is possible for the whole regexp to match at the
start of the string, it I<will> match at the start of the string.  Thus
the first quantifier has to match everything up to the first C<m>.  The
second minimal quantifier matches just one C<m> and the third
quantifier matches the rest of the string.

    $x =~ /(.??)(m{1,2})(.*)$/;  # matches,
                                 # $1 = 'a'
                                 # $2 = 'mm'
                                 # $3 = 'ing republic of Perl'

Just as in the previous regexp, the first quantifier C<.??> can match
earliest at position C<'a'>, so it does.  The second quantifier is
greedy, so it matches C<mm>, and the third matches the rest of the
string.

We can modify principle 3 above to take into account non-greedy
quantifiers:

=over 4

=item *

Principle 3: If there are two or more elements in a regexp, the
leftmost greedy (non-greedy) quantifier, if any, will match as much
(little) of the string as possible while still allowing the whole
regexp to match.  The next leftmost greedy (non-greedy) quantifier, if
any, will try to match as much (little) of the string remaining
available to it as possible, while still allowing the whole regexp to
match.  And so on, until all the regexp elements are satisfied.

=back

Just like alternation, quantifiers are also susceptible to
backtracking.  Here is a step-by-step analysis of the example

    $x = "the cat in the hat";
    $x =~ /^(.*)(at)(.*)$/; # matches,
                            # $1 = 'the cat in the h'
                            # $2 = 'at'
                            # $3 = ''   (0 matches)

=over 4

=item 0

Start with the first letter in the string 't'.

=item 1

The first quantifier '.*' starts out by matching the whole
string 'the cat in the hat'.

=item 2

'a' in the regexp element 'at' doesn't match the end of the
string.  Backtrack one character.

=item 3

'a' in the regexp element 'at' still doesn't match the last
letter of the string 't', so backtrack one more character.

=item 4

Now we can match the 'a' and the 't'.

=item 5

Move on to the third element '.*'.  Since we are at the end of
the string and '.*' can match 0 times, assign it the empty string.

=item 6

We are done!

=back

Most of the time, all this moving forward and backtracking happens
quickly and searching is fast. There are some pathological regexps,
however, whose execution time exponentially grows with the size of the
string.  A typical structure that blows up in your face is of the form

    /(a|b+)*/;

The problem is the nested indeterminate quantifiers.  There are many
different ways of partitioning a string of length n between the C<+>
and C<*>: one repetition with C<b+> of length n, two repetitions with
the first C<b+> length k and the second with length n-k, m repetitions
whose bits add up to length n, etc.  In fact there are an exponential
number of ways to partition a string as a function of its length.  A
regexp may get lucky and match early in the process, but if there is
no match, Perl will try I<every> possibility before giving up.  So be
careful with nested C<*>'s, C<{n,m}>'s, and C<+>'s.  The book
I<Mastering Regular Expressions> by Jeffrey Friedl gives a wonderful
discussion of this and other efficiency issues.


=head2 Possessive quantifiers

Backtracking during the relentless search for a match may be a waste
of time, particularly when the match is bound to fail.  Consider
the simple pattern

    /^\w+\s+\w+$/; # a word, spaces, a word

Whenever this is applied to a string which doesn't quite meet the
pattern's expectations such as S<C<"abc  ">> or S<C<"abc  def ">>,
the regex engine will backtrack, approximately once for each character
in the string.  But we know that there is no way around taking I<all>
of the initial word characters to match the first repetition, that I<all>
spaces must be eaten by the middle part, and the same goes for the second
word.

With the introduction of the I<possessive quantifiers> in Perl 5.10, we
have a way of instructing the regex engine not to backtrack, with the
usual quantifiers with a C<+> appended to them.  This makes them greedy as
well as stingy; once they succeed they won't give anything back to permit
another solution. They have the following meanings:

=over 4

=item *

C<a{n,m}+> means: match at least C<n> times, not more than C<m> times,
as many times as possible, and don't give anything up. C<a?+> is short
for C<a{0,1}+>

=item *

C<a{n,}+> means: match at least C<n> times, but as many times as possible,
and don't give anything up. C<a*+> is short for C<a{0,}+> and C<a++> is
short for C<a{1,}+>.

=item *

C<a{n}+> means: match exactly C<n> times.  It is just there for
notational consistency.

=back

These possessive quantifiers represent a special case of a more general
concept, the I<independent subexpression>, see below.

As an example where a possessive quantifier is suitable we consider
matching a quoted string, as it appears in several programming languages.
The backslash is used as an escape character that indicates that the
next character is to be taken literally, as another character for the
string.  Therefore, after the opening quote, we expect a (possibly
empty) sequence of alternatives: either some character except an
unescaped quote or backslash or an escaped character.

    /"(?:[^"\\]++|\\.)*+"/;


=head2 Building a regexp

At this point, we have all the basic regexp concepts covered, so let's
give a more involved example of a regular expression.  We will build a
regexp that matches numbers.

The first task in building a regexp is to decide what we want to match
and what we want to exclude.  In our case, we want to match both
integers and floating point numbers and we want to reject any string
that isn't a number.

The next task is to break the problem down into smaller problems that
are easily converted into a regexp.

The simplest case is integers.  These consist of a sequence of digits,
with an optional sign in front.  The digits we can represent with