diff --git a/dynamic_programming/regex_match.py b/dynamic_programming/regex_match.py new file mode 100644 index 000000000000..bb2ed2d3a882 --- /dev/null +++ b/dynamic_programming/regex_match.py @@ -0,0 +1,102 @@ +""" +Regex matching check if a text matches wildcard 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 ^ (m + n)), where m is the length of text and n is the length of pattern. + Space complexity: Recursion depth is O(m + n). + + :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 text and not pattern: + return True + + if text and not pattern: + return False + + if not text and pattern and pattern[-1] != '*': + return False + + if not text and pattern and pattern[-1] == '*': + return 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(m * n), where m is the length of text and n is the length of pattern. + Space complexity: O(m * n). + + :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 i in range(1, m + 1): + dp[i][0] = False + + 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] == '.' or pattern[j - 1] == text[i - 1]: + dp[i][j] = dp[i - 1][j - 1] + elif pattern[j - 1] == '*': + dp[i][j] = dp[i][j - 2] or (dp[i - 1][j] and (pattern[j - 2] == '.' or pattern[j - 2] == text[i - 1])) + else: + dp[i][j] = False + + return dp[m][n] + + +if __name__ == "__main__": + import doctest + + doctest.testmod()