


def 						a__			(				A__,      A__				):
			SCREAMING_SNAKE_CASE_		:     Dict					=					len(A__				) + 1
			SCREAMING_SNAKE_CASE_		:     List[str]					=					len(A__				) + 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.
			SCREAMING_SNAKE_CASE_		:     Any					=					[[0 for i in range(A__				)] for j in range(A__				)]

			# since string of zero length match pattern of zero length
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					1

			# since pattern of zero length will never match with string of non-zero length
			for i in range(1,      A__				):
						SCREAMING_SNAKE_CASE_		:     List[Any]					=					0

			# since string of zero length will match with pattern where there
			# is at least one * alternatively
			for j in range(1,      A__				):
						SCREAMING_SNAKE_CASE_		:     List[str]					=					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,      A__				):
						for j in range(1,      A__				):
									if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
												SCREAMING_SNAKE_CASE_		:     Any					=					dp[i - 1][j - 1]

									elif pattern[j - 1] == "*":
												if dp[i][j - 2] == 1:
															SCREAMING_SNAKE_CASE_		:     List[str]					=					1
												elif pattern[j - 2] in (input_string[i - 1], "."):
															SCREAMING_SNAKE_CASE_		:     List[Any]					=					dp[i - 1][j]
												else:
															SCREAMING_SNAKE_CASE_		:     List[str]					=					0
									else:
												SCREAMING_SNAKE_CASE_		:     int					=					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 :")

				lowerCAmelCase__			:      List[Any]								='aab'
				lowerCAmelCase__			:      Dict								='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}""")









def 						a__			(				A__,      A__				):

			def get_matched_characters(A__,      A__				) -> str:
						SCREAMING_SNAKE_CASE_		:     Dict					=					[]
						SCREAMING_SNAKE_CASE_		:     Any					=					min(len(_stra				),      len(_stra				)				) // 2
						for i, l in enumerate(_stra				):
									SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					int(max(0,      i - limit				)				)
									SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					int(min(i + limit + 1,      len(_stra				)				)				)
									if l in _stra[left:right]:
												matched.append(A__				)
												SCREAMING_SNAKE_CASE_		:     List[str]					=					F'''{_stra[0:_stra.index(A__				)]} {_stra[_stra.index(A__				) + 1:]}'''

						return "".join(A__				)

			# matching characters
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					get_matched_characters(A__,      A__				)
			SCREAMING_SNAKE_CASE_		:     int					=					get_matched_characters(A__,      A__				)
			SCREAMING_SNAKE_CASE_		:     Any					=					len(A__				)

			# transposition
			SCREAMING_SNAKE_CASE_		:     Optional[int]					=					(
			    len([(ca, ca) for ca, ca in zip(A__,      A__				) if ca != ca]				) // 2
			)

			if not match_count:
						SCREAMING_SNAKE_CASE_		:     Dict					=					0.0
			else:
						SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					(
						    1
						    / 3
						    * (
						        match_count / len(A__				)
						        + match_count / len(A__				)
						        + (match_count - transpositions) / match_count
						    )
						)

			# common prefix up to 4 characters
			SCREAMING_SNAKE_CASE_		:     List[Any]					=					0
			for ca, ca in zip(stra[:4],      stra[:4]				):
						if ca == ca:
									prefix_len += 1
						else:
									break

			return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				print(jaro_winkler('hello', 'world'))





