Question

Hi I’m going through regular expressions but I’m confused about metacharacters, particularly ‘*’ and ‘?’.

‘*’ is supposed to match the preceding character 0 or more times.

For example, ‘ta*k’ supposedly matches ‘tak’ and ‘tk’.

But I wouldn’t have thought this to be true at all – here’s my reasoning:

for tak:

regexp: I need a ‘t’

string: I have ‘t’

regexp: okay, your next character needs to be an ‘a’

string: yes it is

regexp: okay, keep giving me characters until your character isn’t an ‘a’

string: okay. I’ve just given you ‘k’

regexp: okay, your next character needs to be a ‘k’

string: I don’t have any more characters left!

regexp: fail

for tk:

regexp: I need a ‘t’

string: I have ‘t’

regexp: okay, your next character needs to be an ‘a’

string: no, it’s a ‘k’

regexp: fail

Can someone clarify for me why ‘tak’ and ‘tk’ matches ‘ta*k’?

Answer 1

* does not mean to match a character zero or more times, but an atom zero or more times. A single character is an atom, but so is any grouping.

And * means zero or more. When the regex cursor has “swallowed” the t, the positions are:

in the regex: t|a*k
in the string: t|ak

The regex engine then tries and eats as as much as possible. Here there is one. After it has swallowed it, the positions are:

in the regex: ta*|k
in the string: ta|k

Then the k is swallowed:

in the regex: ta*k|
in the string: tak|

End of regex, match. Note that the string may have other characters behind, the regex engine doesn’t care: it has a match.

In the case where the string is tk, before a* the positions are:

in the regex: t|a*k
in the string: t|k

But * can match an empty set of as, therefore a* is satisfied! Which means the positions then become:

in the regex: ta*|k
in the string: t|k

Rinse, repeat. Now, let’s take taak as an input and ta?k as a regex: this will fail, but let’s see how…

# before first character
regex: |ta?k
input: |taak
# t
regex: t|a?k
input: t|aak
# a?
regex: ta?|k
input: ta|ak
# k? Oops! No...
regex: |ta?k
input: t|aak
# t? Oops! No...
regex: |ta?k
input: ta|ak
# t? Oops! No...
regex: |ta?k
input: taa|k
# t? Oops! No...
regex: |ta?k
input: taak|
# t? Oops! No... And nothing to read anymore
# FAIL

Which is why it is VERY important to make regexes fail FAST.