




from __future__ import annotations

class 		__lowerCAmelCase	:
							def __init__(						self						:Optional[Any]		,      __magic_name__						:int				):







								'''simple docstring'''







								a										=							order

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

								# x[n-1] ... x[n-k]
								a										=							[0.0] * self.order
								# y[n-1] ... y[n-k]
								a										=							[0.0] * self.order
							def       lowerCamelCase__							(						self						:str		,      __magic_name__						:list[float]		,      __magic_name__						:list[float]				):







								'''simple docstring'''







								if len(__magic_name__				) < self.order:
									a										=							[1.0, *a_coeffs]

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

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

								a										=							a_coeffs
								a										=							b_coeffs





							def       lowerCamelCase__							(						self						:Optional[int]		,      __magic_name__						:float				):







								'''simple docstring'''







								a										=							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]
									)

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

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

								a										=							sample
								a										=							result

								return result







from __future__ import annotations

from collections.abc import Iterator

class 		__lowerCAmelCase	:
							def __init__(						self						:Optional[Any]		,      __magic_name__						:int				):







								'''simple docstring'''







								a										=							value
								a										=							None
								a										=							None







class 		__lowerCAmelCase	:
							def __init__(						self						:str		,      __magic_name__						:Node				):







								'''simple docstring'''







								a										=							tree
							def       lowerCamelCase__							(						self						:str		,      __magic_name__						:Node | None				):







								'''simple docstring'''







								if node is None:
									return 0
								return node.value + (
								    self.depth_first_search(node.left				) + self.depth_first_search(node.right				)
								)





							def __iter__(						self						:Tuple				):







								'''simple docstring'''







								yield self.depth_first_search(self.tree				)


if __name__ == "__main__":
		import doctest

		doctest.testmod()

