

'''simple docstring'''




def 							lowerCamelCase			(   UpperCAmelCase__ :      list[int]   ,   UpperCAmelCase__ :      list[int]   ,   UpperCAmelCase__ :      int				)    ->   bool:
							return not any(
							    neighbour == 1 and colored_vertices[i] == color
							    for i, neighbour in enumerate(UpperCAmelCase__				)				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      list[list[int]]   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      list[int]   ,   UpperCAmelCase__ :      int				)    ->   bool:

							# Base Case
							if index == len(UpperCAmelCase__				):
														return True

							# Recursive Step
							for i in range(UpperCAmelCase__				):
														if valid_coloring(graph[index]   ,   UpperCAmelCase__   ,   UpperCAmelCase__				):
																					# Color current vertex
																					lowercase_      :    Union[str, Any]       		= i
																					# Validate coloring
																					if util_color(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   index + 1				):
																												return True
																					# Backtrack
																					lowercase_      :    int       		= -1
							return False




def 							lowerCamelCase			(   UpperCAmelCase__ :      list[list[int]]   ,   UpperCAmelCase__ :      int				)    ->   list[int]:
							lowercase_      :    List[Any]       		= [-1] * len(UpperCAmelCase__				)

							if util_color(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   0				):
														return colored_vertices

							return []






'''simple docstring'''




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    int       		= cos(UpperCAmelCase__				)
							lowercase_      :    Any       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 - _cos) / 2
							lowercase_      :    Optional[int]       		= 1 - _cos

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    List[Any]       		= -2 * _cos
							lowercase_      :    Union[str, Any]       		= 1 - alpha

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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)				)    ->   IIRFilter:
							lowercase_      :    str       		= tau * frequency / samplerate
							lowercase_      :    Optional[int]       		= sin(UpperCAmelCase__				)
							lowercase_      :    Dict       		= cos(UpperCAmelCase__				)
							lowercase_      :    Optional[int]       		= _sin / (2 * q_factor)

							lowercase_      :    Dict       		= (1 + _cos) / 2
							lowercase_      :    str       		= -1 - _cos

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Optional[Any]       		= -2 * _cos
							lowercase_      :    List[Any]       		= 1 - alpha

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




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

							lowercase_      :    str       		= _sin / 2
							lowercase_      :    Any       		= 0
							lowercase_      :    Optional[Any]       		= -ba

							lowercase_      :    Dict       		= 1 + alpha
							lowercase_      :    Union[str, Any]       		= -2 * _cos
							lowercase_      :    Union[str, Any]       		= 1 - alpha

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




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

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

							lowercase_      :    Dict       		= IIRFilter(2				)
							filt.set_coefficients([ba, ba, ba]   ,   [ba, ba, ba]				)
							return filt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float = 1 / sqrt(2				)   ,   )    ->   IIRFilter:
							lowercase_      :    Dict       		= tau * frequency / samplerate
							lowercase_      :    Tuple       		= sin(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= cos(UpperCAmelCase__				)
							lowercase_      :    List[Any]       		= _sin / (2 * q_factor)
							lowercase_      :    Any       		= 10 ** (gain_db / 40)

							lowercase_      :    List[str]       		= 1 + alpha * big_a
							lowercase_      :    List[Any]       		= -2 * _cos
							lowercase_      :    Dict       		= 1 - alpha * big_a
							lowercase_      :    str       		= 1 + alpha / big_a
							lowercase_      :    List[str]       		= -2 * _cos
							lowercase_      :    Tuple       		= 1 - alpha / big_a

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




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

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

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




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

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

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





