Find value of a string given a superstring regex - regex

Question

How can I match for a string that is a substring of a given input string, preferable with regex?
Given a value: A789Lfu891MatchMe2ENOTSTH, construct a regex that would match a string where the string is a substring of the given value.
Expected matches:
MatchMe
ENOTST
891
Expected Non Match
foo
A789L<fu891MatchMe2ENOTSTH_extra
extra_A789L<fu891MatchMe2ENOTSTH
extra_A789L<fu891MatchMe2ENOTSTH_extra
It seems easier for me to do the reverse: /\w*MatchMe\w*/, but I can't wrap my head around this problem.
Something like how SQL would do it:
SELECT * FROM my_table mt WHERE 'A789Lfu891MatchMe2ENOTSTH' LIKE '%' || mt.foo || '%';

Answer 1

Prefix suffixes
You could alternate prefix suffixes, like turn the superstring abcd into a pattern like ^(a|(a)?b|((a)?b)?c|(((a)?b)?c)?d)$. For your example, the pattern has 1253 characters (exactly 2000 fewer than #tobias_k's).
Python code to produce the regex, can then be tested with tobias_k's code (try it online):
from itertools import accumulate
t = "A789Lfu891MatchMe2ENOTSTH"
p = '^(' + '|'.join(accumulate(t, '({})?{}'.format)) + ')$'
Suffix prefixes
Suffix prefixes look nicer and match faster: ^(a(b(c(d)?)?)?|b(c(d)?)?|c(d)?|d)$. Sadly the generating code is less elegant.
Divide and conquer
For a shorter regex, we can use divide and conquer. For example for the superstring abcdefg, every substring falls into one of three cases:
Contains the middle character (the d). Pattern for that: ((a?b)?c)?d(e(fg?)?)?
Is left of that middle character. So recursively build a regex for the superstring abc: a|a?bc?|c.
Is right of that middle character. So recursively build a regex for the superstring efg: e|e?fg?|g.
And then make an alternation of those three cases:
a|a?bc?|c|((a?b)?c)?d(e(fg?)?)?|e|e?fg?|g
Regex length will be Θ(n log n) instead of our previous Θ(n2).
The result for your superstring example of 25 characters is this regex with 301 characters:
^(A|A?78?|8|((A?7)?8)?9(Lf?)?|Lf?|f|(((((A?7)?8)?9)?L)?f)?u(8(9(1(Ma?)?)?)?)?|89?|9|(8?9)?1(Ma?)?|Ma?|a|(((((((((((A?7)?8)?9)?L)?f)?u)?8)?9)?1)?M)?a)?t(c(h(M(e(2(E(N(O(T(S(TH?)?)?)?)?)?)?)?)?)?)?)?|c|c?hM?|M|((c?h)?M)?e(2E?)?|2E?|E|(((((c?h)?M)?e)?2)?E)?N(O(T(S(TH?)?)?)?)?|OT?|T|(O?T)?S(TH?)?|TH?|H)$
Benchmark
Speed benchmarks don't really make that much sense, as in reality we'd just do a regular substring check (in Python s in t), but let's do one anyway.
Results for matching all substrings of your superstring, using Python 3.9.6 on my PC:
1.09 ms just_all_substrings
25.18 ms prefix_suffixes
3.47 ms suffix_prefixes
3.46 ms divide_and_conquer
And on TIO and their "Python 3.8 (pre-release)" with quite different results:
0.30 ms just_all_substrings
46.90 ms prefix_suffixes
2.24 ms suffix_prefixes
2.95 ms divide_and_conquer
Regex lengths (also printed by the below benchmark code):
3253 characters - just_all_substrings
1253 characters - prefix_suffixes
1253 characters - suffix_prefixes
301 characters - divide_and_conquer
Benchmark code (Try it online!):
from timeit import repeat
import re
from itertools import accumulate
def just_all_substrings(t):
return "^(" + '|'.join(t[i:k] for i in range(0, len(t))
for k in range(i+1, len(t)+1)) + ")$"
def prefix_suffixes(t):
return '^(' + '|'.join(accumulate(t, '({})?{}'.format)) + ')$'
def suffix_prefixes(t):
return '^(' + '|'.join(list(accumulate(t[::-1], '{1}({0})?'.format))[::-1]) + ')$'
def divide_and_conquer(t):
def suffixes(t):
# Example: abc => ((a?b)?c)?
regex = f'{t[0]}?'
for c in t[1:]:
regex = f'({regex}{c})?'
return regex
def prefixes(t):
# Example: efg => (e(fg?)?)?
regex = f'{t[-1]}?'
for c in t[-2::-1]:
regex = f'({c}{regex})?'
return regex
def superegex(t):
n = len(t)
if n == 1:
return t
if n == 2:
return f'{t}?|{t[1]}'
mid = n // 2
contain = suffixes(t[:mid]) + t[mid] + prefixes(t[mid+1:])
left = superegex(t[:mid])
right = superegex(t[mid+1:])
return '|'.join([left, contain, right])
return '^(' + superegex(t) + ')$'
creators = just_all_substrings, prefix_suffixes, suffix_prefixes, divide_and_conquer,
t = "A789Lfu891MatchMe2ENOTSTH"
substrings = [t[start:stop]
for start in range(len(t))
for stop in range(start+1, len(t)+1)]
def test(p):
match = re.compile(p).match
return all(map(re.compile(p).match, substrings))
for creator in creators:
print(test(creator(t)), creator.__name__)
print()
print('Regex lengths:')
for creator in creators:
print('%5d characters -' % len(creator(t)), creator.__name__)
print()
for _ in range(3):
for creator in creators:
p = creator(t)
number = 10
time = min(repeat(lambda: test(p), number=number)) / number
print('%5.2f ms ' % (time * 1e3), creator.__name__)
print()

Answer 2

One way to "construct" such a regex would be to build a disjunction of all possible substrings of the original value. Example in Python:
import re
t = "A789Lfu891MatchMe2ENOTSTH"
p = "^(" + '|'.join(t[i:k] for i in range(0, len(t))
for k in range(i+1, len(t)+1)) + ")$"
good = ["MatchMe", "ENOTST", "891"]
bad = ["foo", "A789L<fu891MatchMe2ENOTSTH_extra",
"extra_A789L<fu891MatchMe2ENOTSTH",
"extra_A789L<fu891MatchMe2ENOTSTH_extra"]
assert all(re.match(p, s) is not None for s in good)
assert all(re.match(p, s) is None for s in bad)
For the value "abcd", this would e.g. be "^(a|ab|abc|abcd|b|bc|bcd|c|cd|d)$"; for the given example it's a bit longer, with 3253 characters...