Add wildcard pattern matching using dynamic programming

dynamic_programming/regular_expression.py

@@ -0,0 +1,103 @@
+"""
+Implementation of regular expression matching with support for '.' and '*'.
+'.' Matches any single character.
+'*' Matches zero or more of the preceding element.
+The matching should cover the entire input string (not partial).
+
+"""
+
+
+def string_match_pattern(input_string: str, pattern: str) -> bool:
+    """
+    using bottom-up dynamic programming solution for matching the input
+    string with a given pattern.
+
+    Runtime: O(len(input_string)*len(pattern))
+
+    Arguments
+    --------
+    input_string: str, any string which should be compared with pattern
+    pattern: str, the string that has to be used as pattern and should contain
+    '.' for single character match and '*' for zero or more of preceding character
+    match
+
+    Note
+    ----
+    the pattern can not start with a '*',
+    because there should be at least one character before *
+
+    Returns
+    -------
+    the bool value denoting whether given string follows the pattern
+
+    Examples
+    -------
+    >>> string_match_pattern("aab", "c*a*b")
+    True
+    >>> string_match_pattern("aaa", "aa")
+    False
+    >>> string_match_pattern("aaab", "aa*")
+    False
+    >>> string_match_pattern("aaab", ".*")
+    True
+    >>> string_match_pattern("a", "bbbb")
+    False
+    >>> string_match_pattern("", "bbbb")
+    False
+    >>> string_match_pattern("a", "")
+    False
+    """
+
+    len_string = len(input_string) + 1
+    len_pattern = len(pattern) + 1
+
+    # dp is a 2d matrix where dp[i][j] denotes whether prefix string of
+    # length i of input_string matches with prefix string of length j of
+    # given pattern
+    dp = [[0 for i in range(len_pattern)] for j in range(len_string)]
+
+    # since string of zero length match pattern of zero length
+    dp[0][0] = 1
+
+    # since pattern of zero length will never match with string of non-zero length
+    for i in range(1, len_string):
+        dp[i][0] = 0
+
+    # since string of zero length will match with pattern where there
+    # is at least one * alternatively
+    for j in range(1, len_pattern):
+        dp[0][j] = dp[0][j - 2] if pattern[j - 1] == "*" else 0
+
+    # now using bottom-up approach to find for all remaining lengths
+    for i in range(1, len_string):
+        for j in range(1, len_pattern):
+            if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
+                dp[i][j] = dp[i - 1][j - 1]
+
+            elif pattern[j - 1] == "*":
+                if dp[i][j - 2] == 1:
+                    dp[i][j] = 1
+                elif pattern[j - 2] in (input_string[i - 1], "."):
+                    dp[i][j] = dp[i - 1][j]
+                else:
+                    dp[i][j] = 0
+            else:
+                dp[i][j] = 0
+
+    return bool(dp[-1][-1])
+
+
+if __name__ == "__main__":
+
+    # inputing the strings
+    # input_string = input("input a string :")
+    # pattern = input("input a pattern :")
+
+    input_string = "aab"
+    pattern = "c*a*b"
+
+    # using function to check whether given string matches the given pattern
+    if string_match_pattern(input_string, pattern):
+        print(f"{input_string} matches the given pattern {pattern}")
+    else:
+        print(f"{input_string} does not match with the given pattern {pattern}")