





def 				lowerCAmelCase_			(      SCREAMING_SNAKE_CASE       :							Dict    ,						SCREAMING_SNAKE_CASE       :							Optional[Any]   ):


							'''simple docstring'''







							__lowerCamelCase      :      Optional[Any]         =len(__lowerCAmelCase   ) + 1
							__lowerCamelCase      :      int         =len(__lowerCAmelCase   ) + 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.
							__lowerCamelCase      :      Dict         =[[0 for i in range(__lowerCAmelCase   )] for j in range(__lowerCAmelCase   )]

							# since string of zero length match pattern of zero length
							__lowerCamelCase      :      Dict         =1

							# since pattern of zero length will never match with string of non-zero length
							for i in range(1    ,						__lowerCAmelCase   ):
														__lowerCamelCase      :      Union[str, Any]         =0

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

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

							_UpperCamelCase							=      "aab"
							_UpperCamelCase							=      "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}''')











"""simple docstring"""





def 				lowerCAmelCase_			(      SCREAMING_SNAKE_CASE       :							list    ,						SCREAMING_SNAKE_CASE       :							list    ,						SCREAMING_SNAKE_CASE       :							int   ):


							'''simple docstring'''







							__lowerCamelCase      :      Optional[Any]         =len(SCREAMING_SNAKE_CASE   )
							__lowerCamelCase      :      Union[str, Any]         =[[0] * n for i in range(SCREAMING_SNAKE_CASE   )]
							for i in range(SCREAMING_SNAKE_CASE   ):
														__lowerCamelCase      :      Union[str, Any]         =y_points[i]

							for i in range(2    ,						SCREAMING_SNAKE_CASE   ):
														for j in range(SCREAMING_SNAKE_CASE    ,						SCREAMING_SNAKE_CASE   ):
																					__lowerCamelCase      :      List[Any]         =(
																					    (xa - x_points[j - i + 1]) * q[j][i - 1]
																					    - (xa - x_points[j]) * q[j - 1][i - 1]
																					) / (x_points[j] - x_points[j - i + 1])

							return [q[n - 1][n - 1], q]


if __name__ == "__main__":
							import doctest

							doctest.testmod()




