Add: Two Regex match algorithm (Recursive & DP) (TheAlgorithms#6321)

* Add recursive solution to regex_match.py

* Add dp solution to regex_match.py

* Add link to regex_match.py

* Minor edit

* Minor change

* Minor change

* Update dynamic_programming/regex_match.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update dynamic_programming/regex_match.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Fix ruff formatting in if statements

* Update dynamic_programming/regex_match.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

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Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

dynamic_programming/regex_match.py

@@ -0,0 +1,97 @@
+"""
+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()