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"""

Regex matching check if a text matches pattern or not.

Pattern:

'.' Matches any single character.

'*' Matches zero or more of the preceding element.

More info:

https://medium.com/trick-the-interviwer/regular-expression-matching-9972eb74c03

"""

def recursive_match(text: str, pattern: str) -> bool:

"""

Recursive matching algorithm.

Time complexity: O(2 ^ (|text| + |pattern|))

Space complexity: Recursion depth is O(|text| + |pattern|).

:param text: Text to match.

:param pattern: Pattern to match.

:return: True if text matches pattern, False otherwise.

>>> recursive_match('abc', 'a.c')

True

>>> recursive_match('abc', 'af*.c')

True

>>> recursive_match('abc', 'a.c*')

True

>>> recursive_match('abc', 'a.c*d')

False

>>> recursive_match('aa', '.*')

True

"""

if not pattern:

return not text

if not text:

return pattern[-1] == "*" and recursive_match(text, pattern[:-2])

if text[-1] == pattern[-1] or pattern[-1] == ".":

return recursive_match(text[:-1], pattern[:-1])

if pattern[-1] == "*":

return recursive_match(text[:-1], pattern) or recursive_match(

text, pattern[:-2]

)

return False

def dp_match(text: str, pattern: str) -> bool:

"""

Dynamic programming matching algorithm.

Time complexity: O(|text| * |pattern|)

Space complexity: O(|text| * |pattern|)

:param text: Text to match.

:param pattern: Pattern to match.

:return: True if text matches pattern, False otherwise.

>>> dp_match('abc', 'a.c')

True

>>> dp_match('abc', 'af*.c')

True

>>> dp_match('abc', 'a.c*')

True

>>> dp_match('abc', 'a.c*d')

False

>>> dp_match('aa', '.*')

True

"""

m = len(text)

n = len(pattern)

dp = [[False for _ in range(n + 1)] for _ in range(m + 1)]

dp[0][0] = True

for j in range(1, n + 1):

dp[0][j] = pattern[j - 1] == "*" and dp[0][j - 2]

for i in range(1, m + 1):

for j in range(1, n + 1):

if pattern[j - 1] in {".", text[i - 1]}:

dp[i][j] = dp[i - 1][j - 1]

elif pattern[j - 1] == "*":

dp[i][j] = dp[i][j - 2]

if pattern[j - 2] in {".", text[i - 1]}:

dp[i][j] |= dp[i - 1][j]

else:

dp[i][j] = False

return dp[m][n]

if __name__ == "__main__":

import doctest

doctest.testmod()

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