





'''simple docstring'''

from __future__ import annotations

class       UpperCAmelCase :




		def __init__(self      :	Tuple							,			A__      :	int				)					-> None:
						lowercase         = order

						# a_{0} ... a_{k}
						lowercase         = [1.0] + [0.0] * order
						# b_{0} ... b_{k}
						lowercase         = [1.0] + [0.0] * order

						# x[n-1] ... x[n-k]
						lowercase         = [0.0] * self.order
						# y[n-1] ... y[n-k]
						lowercase         = [0.0] * self.order




		def 				UpperCAmelCase__   (self      :	Dict							,			A__      :	list[float]							,			A__      :	list[float]				)					-> None:
						if len(A__				) < self.order:
										lowercase         = [1.0, *a_coeffs]

						if len(A__				) != self.order + 1:
										lowercase         = (
										    f'Expected a_coeffs to have {self.order + 1} elements '
										    f'for {self.order}-order filter, got {len(A__				)}'
										)
										raise ValueError(A__				)

						if len(A__				) != self.order + 1:
										lowercase         = (
										    f'Expected b_coeffs to have {self.order + 1} elements '
										    f'for {self.order}-order filter, got {len(A__				)}'
										)
										raise ValueError(A__				)

						lowercase         = a_coeffs
						lowercase         = b_coeffs





		def 				UpperCAmelCase__   (self      :	List[Any]							,			A__      :	float				)					-> float:
						lowercase         = 0.0

						# Start at index 1 and do index 0 at the end.
						for i in range(1							,			self.order + 1				):
										result += (
										    self.b_coeffs[i] * self.input_history[i - 1]
										    - self.a_coeffs[i] * self.output_history[i - 1]
										)

						lowercase         = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

						lowercase         = self.input_history[:-1]
						lowercase         = self.output_history[:-1]

						lowercase         = sample
						lowercase         = result

						return result











'''simple docstring'''

# Algorithm for the pigeonhole sorting









def 							UpperCAmelCase_    (	lowerCAmelCase_							):

				"""simple docstring"""






				lowercase         = min(lowerCAmelCase_							)  # min() finds the minimum value
				lowercase         = max(lowerCAmelCase_							)  # max() finds the maximum value

				lowercase         = max_val - min_val + 1  # size is difference of max and min values plus one

				# list of pigeonholes of size equal to the variable size
				lowercase         = [0] * size

				# Populate the pigeonholes.
				for x in a:
								assert isinstance(lowerCAmelCase_		,							lowerCAmelCase_							), "integers only please"
								holes[x - min_val] += 1

				# Putting the elements back into the array in an order.
				lowercase         = 0
				for count in range(lowerCAmelCase_							):
								while holes[count] > 0:
												holes[count] -= 1
												lowercase         = count + min_val
												i += 1







def 							UpperCAmelCase_    (	):

				"""simple docstring"""






				lowercase         = [8, 3, 2, 7, 4, 6, 8]
				pigeonhole_sort(lowerCAmelCase_							)
				print("Sorted order is:"		,							" ".join(lowerCAmelCase_							)							)


if __name__ == "__main__":
			main()




