

def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase					)							->     bool:



  """simple docstring"""






  if graph[path[curr_ind - 1]][next_ver] == 0:
    return False

  # 2. Validate that next vertex is not already in path
  return not any(vertex == next_ver for vertex in path					)



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase					)							->     bool:



  """simple docstring"""






  if curr_ind == len(_UpperCamelCase					):
    # return whether path exists between current and starting vertices
    return graph[path[curr_ind - 1]][path[0]] == 1

  # Recursive Step
  for next_ver in range(0			,	len(_UpperCamelCase					)					):
    if valid_connection(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase					):
      # Insert current vertex  into path as next transition
      _snake_case						=							next_ver
      # Validate created path
      if util_hamilton_cycle(_UpperCamelCase			,	_UpperCamelCase			,	curr_ind + 1					):
        return True
      # Backtrack
      _snake_case						=							-1
  return False



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase = 0					)							->     list[int]:



  """simple docstring"""






  _snake_case						=							[-1] * (len(_UpperCamelCase					) + 1)
  # initialize start and end of path with starting index
  _snake_case						=							_snake_case						=							start_index
  # evaluate and if we find answer return path either return empty array
  return path if util_hamilton_cycle(_UpperCamelCase			,	_UpperCamelCase			,	1					) else []




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							(1 - _cos) / 2
  _snake_case						=							1 - _cos

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							(1 + _cos) / 2
  _snake_case						=							-1 - _cos

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							_sin / 2
  _snake_case						=							0
  _snake_case						=							-ba

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							1 - alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 + alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([ba, ba, ba]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)

  _snake_case						=							1 + alpha * big_a
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha * big_a
  _snake_case						=							1 + alpha / big_a
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha / big_a

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

  _snake_case						=							big_a * (pmc + aaa)
  _snake_case						=							2 * big_a * mpc
  _snake_case						=							big_a * (pmc - aaa)
  _snake_case						=							ppmc + aaa
  _snake_case						=							-2 * pmpc
  _snake_case						=							ppmc - aaa

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

  _snake_case						=							big_a * (ppmc + aaa)
  _snake_case						=							-2 * big_a * pmpc
  _snake_case						=							big_a * (ppmc - aaa)
  _snake_case						=							pmc + aaa
  _snake_case						=							2 * mpc
  _snake_case						=							pmc - aaa

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt

