Add dp solution to regex_match.py

dynamic_programming/regex_match.py

@@ -25,6 +25,8 @@ def recursive_match(text: str, pattern: str) -> bool:
     True
     >>> recursive_match('abc', 'a.c*d')
     False
+    >>> recursive_match('aa', '.*')
+    True
     """
     if not text and not pattern:
         return True
@@ -47,6 +49,51 @@ def recursive_match(text: str, pattern: str) -> bool:
     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