

from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float = 1 / sqrt(2	)	)				->    IIRFilter:
				_UpperCAmelCase    :						Dict							=      tau * frequency / samplerate
				_UpperCAmelCase    :						List[str]							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						Tuple							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						Optional[Any]							=      _sin / (2 * q_factor)

				_UpperCAmelCase    :						List[Any]							=      (1 - _cos) / 2
				_UpperCAmelCase    :						List[Any]							=      1 - _cos

				_UpperCAmelCase    :						int							=      1 + alpha
				_UpperCAmelCase    :						Tuple							=      -2 * _cos
				_UpperCAmelCase    :						Optional[Any]							=      1 - alpha

				_UpperCAmelCase    :						Union[str, Any]							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float = 1 / sqrt(2	)	)				->    IIRFilter:
				_UpperCAmelCase    :						Optional[int]							=      tau * frequency / samplerate
				_UpperCAmelCase    :						List[Any]							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						Any							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						str							=      _sin / (2 * q_factor)

				_UpperCAmelCase    :						List[Any]							=      (1 + _cos) / 2
				_UpperCAmelCase    :						Dict							=      -1 - _cos

				_UpperCAmelCase    :						int							=      1 + alpha
				_UpperCAmelCase    :						Any							=      -2 * _cos
				_UpperCAmelCase    :						int							=      1 - alpha

				_UpperCAmelCase    :						Any							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float = 1 / sqrt(2	)	)				->    IIRFilter:
				_UpperCAmelCase    :						Tuple							=      tau * frequency / samplerate
				_UpperCAmelCase    :						Any							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						List[Any]							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						Union[str, Any]							=      _sin / (2 * q_factor)

				_UpperCAmelCase    :						Union[str, Any]							=      _sin / 2
				_UpperCAmelCase    :						List[str]							=      0
				_UpperCAmelCase    :						Tuple							=      -ba

				_UpperCAmelCase    :						Union[str, Any]							=      1 + alpha
				_UpperCAmelCase    :						Tuple							=      -2 * _cos
				_UpperCAmelCase    :						Tuple							=      1 - alpha

				_UpperCAmelCase    :						int							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float = 1 / sqrt(2	)	)				->    IIRFilter:
				_UpperCAmelCase    :						Any							=      tau * frequency / samplerate
				_UpperCAmelCase    :						Union[str, Any]							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						Union[str, Any]							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						Optional[Any]							=      _sin / (2 * q_factor)

				_UpperCAmelCase    :						Any							=      1 - alpha
				_UpperCAmelCase    :						int							=      -2 * _cos
				_UpperCAmelCase    :						Any							=      1 + alpha

				_UpperCAmelCase    :						Optional[Any]							=      IIRFilter(2	)
				filt.set_coefficients([ba, ba, ba]					, [ba, ba, ba]	)
				return filt

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float					, lowerCAmelCase:					float = 1 / sqrt(2	)					, )				->    IIRFilter:
				_UpperCAmelCase    :						Any							=      tau * frequency / samplerate
				_UpperCAmelCase    :						Optional[int]							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						Union[str, Any]							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						Optional[int]							=      _sin / (2 * q_factor)
				_UpperCAmelCase    :						List[str]							=      10 ** (gain_db / 40)

				_UpperCAmelCase    :						Dict							=      1 + alpha * big_a
				_UpperCAmelCase    :						Union[str, Any]							=      -2 * _cos
				_UpperCAmelCase    :						Optional[Any]							=      1 - alpha * big_a
				_UpperCAmelCase    :						int							=      1 + alpha / big_a
				_UpperCAmelCase    :						str							=      -2 * _cos
				_UpperCAmelCase    :						List[Any]							=      1 - alpha / big_a

				_UpperCAmelCase    :						Optional[Any]							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float					, lowerCAmelCase:					float = 1 / sqrt(2	)					, )				->    IIRFilter:
				_UpperCAmelCase    :						Tuple							=      tau * frequency / samplerate
				_UpperCAmelCase    :						Dict							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						Optional[int]							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						str							=      _sin / (2 * q_factor)
				_UpperCAmelCase    :						str							=      10 ** (gain_db / 40)
				_UpperCAmelCase    :						Any							=      (big_a + 1) - (big_a - 1) * _cos
				_UpperCAmelCase    :						int							=      (big_a + 1) + (big_a - 1) * _cos
				_UpperCAmelCase    :						List[str]							=      (big_a - 1) - (big_a + 1) * _cos
				_UpperCAmelCase    :						Dict							=      (big_a - 1) + (big_a + 1) * _cos
				_UpperCAmelCase    :						Union[str, Any]							=      2 * sqrt(lowerCAmelCase	) * alpha

				_UpperCAmelCase    :						int							=      big_a * (pmc + aaa)
				_UpperCAmelCase    :						Optional[int]							=      2 * big_a * mpc
				_UpperCAmelCase    :						str							=      big_a * (pmc - aaa)
				_UpperCAmelCase    :						List[Any]							=      ppmc + aaa
				_UpperCAmelCase    :						int							=      -2 * pmpc
				_UpperCAmelCase    :						int							=      ppmc - aaa

				_UpperCAmelCase    :						Optional[Any]							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt





def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int					, lowerCAmelCase:					float					, lowerCAmelCase:					float = 1 / sqrt(2	)					, )				->    IIRFilter:
				_UpperCAmelCase    :						List[Any]							=      tau * frequency / samplerate
				_UpperCAmelCase    :						int							=      sin(lowerCAmelCase	)
				_UpperCAmelCase    :						List[str]							=      cos(lowerCAmelCase	)
				_UpperCAmelCase    :						List[Any]							=      _sin / (2 * q_factor)
				_UpperCAmelCase    :						Union[str, Any]							=      10 ** (gain_db / 40)
				_UpperCAmelCase    :						int							=      (big_a + 1) - (big_a - 1) * _cos
				_UpperCAmelCase    :						Optional[Any]							=      (big_a + 1) + (big_a - 1) * _cos
				_UpperCAmelCase    :						Dict							=      (big_a - 1) - (big_a + 1) * _cos
				_UpperCAmelCase    :						List[Any]							=      (big_a - 1) + (big_a + 1) * _cos
				_UpperCAmelCase    :						Tuple							=      2 * sqrt(lowerCAmelCase	) * alpha

				_UpperCAmelCase    :						Any							=      big_a * (ppmc + aaa)
				_UpperCAmelCase    :						str							=      -2 * big_a * pmpc
				_UpperCAmelCase    :						List[str]							=      big_a * (ppmc - aaa)
				_UpperCAmelCase    :						Any							=      pmc + aaa
				_UpperCAmelCase    :						Any							=      2 * mpc
				_UpperCAmelCase    :						Union[str, Any]							=      pmc - aaa

				_UpperCAmelCase    :						Tuple							=      IIRFilter(2	)
				filt.set_coefficients([aa, aa, aa]					, [ba, ba, ba]	)
				return filt





def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					str					, lowerCAmelCase:					str	)				->    bool:
				_UpperCAmelCase    :						Optional[Any]							=      len(lowerCAmelCase	) + 1
				_UpperCAmelCase    :						Optional[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.
				_UpperCAmelCase    :						List[str]							=      [[0 for i in range(lowerCAmelCase	)] for j in range(lowerCAmelCase	)]

				# since string of zero length match pattern of zero length
				_UpperCAmelCase    :						List[Any]							=      1

				# since pattern of zero length will never match with string of non-zero length
				for i in range(1					, lowerCAmelCase	):
								_UpperCAmelCase    :						Dict							=      0

				# since string of zero length will match with pattern where there
				# is at least one * alternatively
				for j in range(1					, lowerCAmelCase	):
								_UpperCAmelCase    :						Tuple							=      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] == ".":
																_UpperCAmelCase    :						Optional[Any]							=      dp[i - 1][j - 1]

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

					SCREAMING_SNAKE_CASE_            = 'aab'
					SCREAMING_SNAKE_CASE_            = '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}''')


