Add wildcard pattern matching using dynamic programming (#5334)

* Added regular expression implimentation using dp

* replaced input() with example values

* Apply suggestions from code review

Co-authored-by: Christian Clauss <cclauss@me.com>

* changed returning value to bool and added test cases

* added doctest

Co-authored-by: John Law <johnlaw.po@gmail.com>

* added test cases

* Apply suggestions from code review

Co-authored-by: John Law <johnlaw.po@gmail.com>

* shifted to strings

* Changed filename

* Update function name to match_pattern

Co-authored-by: John Law <johnlaw.po@gmail.com>

* Update function name to match_pattern

Co-authored-by: John Law <johnlaw.po@gmail.com>

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>

strings/wildcard_pattern_matching.py

@@ -0,0 +1,112 @@
+"""
+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 match_pattern(input_string: str, pattern: str) -> bool:
+    """
+    uses 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 the pattern
+    pattern: str, the string that represents a pattern and may contain
+    '.' for single character matches and '*' for zero or more of preceding character
+    matches
+
+    Note
+    ----
+    the pattern cannot start with a '*',
+    because there should be at least one character before *
+
+    Returns
+    -------
+    A Boolean denoting whether the given string follows the pattern
+
+    Examples
+    -------
+    >>> match_pattern("aab", "c*a*b")
+    True
+    >>> match_pattern("dabc", "*abc")
+    False
+    >>> match_pattern("aaa", "aa")
+    False
+    >>> match_pattern("aaa", "a.a")
+    True
+    >>> match_pattern("aaab", "aa*")
+    False
+    >>> match_pattern("aaab", ".*")
+    True
+    >>> match_pattern("a", "bbbb")
+    False
+    >>> match_pattern("", "bbbb")
+    False
+    >>> match_pattern("a", "")
+    False
+    >>> match_pattern("", "")
+    True
+    """
+
+    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" stands for dynamic programming.
+    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__":
+    import doctest
+
+    doctest.testmod()
+    # 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 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}")