






from __future__ import annotations


class 					_snake_case						:






	def __init__(		self					,UpperCamelCase       )						->    None:
					snake_case__      :Optional[Any]         =   order

					# a_{0} ... a_{k}
					snake_case__      :Any         =   [1.0] + [0.0] * order
					# b_{0} ... b_{k}
					snake_case__      :List[Any]         =   [1.0] + [0.0] * order

					# x[n-1] ... x[n-k]
					snake_case__      :int         =   [0.0] * self.order
					# y[n-1] ... y[n-k]
					snake_case__      :Any         =   [0.0] * self.order






	def    lowerCAmelCase_							(		self					,UpperCamelCase					,UpperCamelCase       )						->    None:
					if len(UpperCamelCase       ) < self.order:
									snake_case__      :Tuple         =   [1.0, *a_coeffs]

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

					if len(UpperCamelCase       ) != self.order + 1:
									snake_case__      :Union[str, Any]         =   (
									    f'Expected b_coeffs to have {self.order + 1} elements '
									    f'for {self.order}-order filter, got {len(UpperCamelCase       )}'
									)
									raise ValueError(UpperCamelCase       )

					snake_case__      :List[str]         =   a_coeffs
					snake_case__      :List[str]         =   b_coeffs






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    float:
					snake_case__      :Tuple         =   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]
									)

					snake_case__      :str         =   (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

					snake_case__      :str         =   self.input_history[:-1]
					snake_case__      :List[str]         =   self.output_history[:-1]

					snake_case__      :Any         =   sample
					snake_case__      :str         =   result

					return result







from __future__ import annotations


class 					_snake_case						:






	def __init__(		self					,UpperCamelCase       )						->    None:
					snake_case__      :Union[str, Any]         =   data
					snake_case__      :Node | None         =   None
					snake_case__      :Node | None         =   None





def 					lowercase_ (    __snake_case     :							Node | None      )     -> None:  # In Order traversal of the tree





				'''simple docstring'''


				if tree:
								display(tree.left      )
								print(tree.data      )
								display(tree.right      )





def 					lowercase_ (    __snake_case     :							Node | None      )     -> int:





				'''simple docstring'''


				return 1 + max(depth_of_tree(tree.left      )	,	depth_of_tree(tree.right      )      ) if tree else 0





def 					lowercase_ (    __snake_case     :							Node      )     -> bool:





				'''simple docstring'''


				if not tree:
								return True
				if tree.left and tree.right:
								return is_full_binary_tree(tree.left      ) and is_full_binary_tree(tree.right      )
				else:
								return not tree.left and not tree.right





def 					lowercase_ (    )     -> None:  # Main function for testing.





				'''simple docstring'''


				snake_case__      :Dict         =   Node(1      )
				snake_case__      :int         =   Node(2      )
				snake_case__      :Optional[Any]         =   Node(3      )
				snake_case__      :Tuple         =   Node(4      )
				snake_case__      :str         =   Node(5      )
				snake_case__      :Optional[Any]         =   Node(6      )
				snake_case__      :List[Any]         =   Node(7      )
				snake_case__      :List[str]         =   Node(8      )
				snake_case__      :Tuple         =   Node(9      )

				print(is_full_binary_tree(__snake_case      )      )
				print(depth_of_tree(__snake_case      )      )
				print("Tree is: "      )
				display(__snake_case      )


if __name__ == "__main__":
	main()