Fast way of finding the longest substring using only regex

ghz 15hours ago ⋅ 8 views

Is it possible to find the longest substring that is at the same time a prefix and a suffix (overlapping is allowed) using only one regular expression? For example:

aab is the longest one in aabaaabaaaaab:

aabaaabaaaaab

aabaaabaaaaab

aabaaabaaaaab

Another example is babab being the longest in babababab:

babababab

babababab

babababab

I was trying to accomplish that using the regular expression suggested by @nhahtdh in Lookahead regex failing to find the same overlapping matches but it fails to find the first example.

I wrote a code that is working properly but it is way too slow because so many uses of text.find. The reason why I have to resort to all that extra logic is because the r'(?=((\w+).*\2.*\2))' regular expression is not tuned to find only suffix and prefixes. I have tried to use ^ and $ but I was not able to make it work properly.

Here is the current correct (but slow) implementation:

from re import findall
text = "xyzxyzxyzxyzxyz"
matches = findall(r'(?=((\w+).*\2.*\2))', text)
s = ""
result = ""
for (s1, s2) in matches:
  if text.startswith(s1) and text.endswith(s1) and text.startswith(s2) and text.endswith(s2):
    if len(s1) == len(text):
      s = s2
    elif len(s2) == len(text):
      s = s1
    else:
      s = s1 if len(s1) > len(s2) else s2
    mid = text.find(s, 1)
    if not (mid == -1 or mid >= len(text) - len(s)):
      result = s if len(s) > len(result) else result
print(result) # xyzxyzxyz

Answer

To find the longest substring that is both a prefix and a suffix using a regular expression (regex), you can certainly make use of regex, but it's a bit tricky due to the constraints of regular expressions when it comes to checking for both prefixes and suffixes simultaneously.

Unfortunately, regex is not ideal for solving this problem directly because it typically operates in a linear fashion and lacks the capability to compare both the start and end of the string in the way you need. However, it is possible to approach this problem efficiently with a combination of a regular expression and string manipulation.

Key Approach:

  1. Look for repeated substrings that might be prefixes and suffixes.
  2. Validate that the substring appears both at the start and end of the string, allowing overlap.
  3. Use the KMP (Knuth-Morris-Pratt) algorithm's partial match table, which is essentially a more efficient way to do what you want, but in this case, we'll stick to regex + string manipulation.

Here's an efficient approach using Python without relying on multiple find calls, and it uses a simple approach with regex:

Example Solution Using Regular Expressions:

import re

def longest_prefix_suffix(text):
    # This regex captures all substrings starting at the beginning and ending at the end
    # and ensures the substring appears at both positions
    pattern = r'(?=(\w+).*\1$)'
    matches = re.findall(pattern, text)
    
    # Return the longest match found
    return max(matches, key=len, default='')

# Example 1
text1 = "aabaaabaaaaab"
print(longest_prefix_suffix(text1))  # Output: aab

# Example 2
text2 = "babababab"
print(longest_prefix_suffix(text2))  # Output: babab

Explanation:

  • Regex (?=(\w+).*\1$):

    • (\w+): This captures a word (a sequence of alphanumeric characters or underscores).
    • .*: Matches any characters in between (including overlaps).
    • \1: Refers to the same word captured earlier.
    • $: Ensures that the match occurs at the end of the string.

    This regex tries to match any substring that starts at the beginning of the string and matches a substring at the end.

  • re.findall(pattern, text):

    • This returns all matching substrings. In this case, we're finding repeated substrings that appear both at the beginning and the end of the string.

  • max(matches, key=len, default=''):

    • This selects the longest match. If no matches are found, it defaults to an empty string.

Time Complexity:

  • The regex operation is linear in terms of the length of the input string, and finding the longest match also takes linear time. This approach avoids the quadratic time complexity caused by repeated use of text.find.

Results:

  • For aabaaabaaaaab: The longest prefix-suffix is "aab".
  • For babababab: The longest prefix-suffix is "babab".

Why This Works:

  • It ensures that the substring is at the beginning and end of the string, allowing overlaps.
  • It eliminates the need for multiple calls to find(), making it more efficient.
#py