
from __future__ import annotations






class UpperCAmelCase   :





   '''simple docstring'''


   def __init__(					self     :							Any			,			lowerCAmelCase_     :							int     ):

      """simple docstring"""
      _A:  Optional[Any]					=       order

      # a_{0} ... a_{k}
      _A:  Optional[Any]					=       [1.0] + [0.0] * order
      # b_{0} ... b_{k}
      _A:  Tuple					=       [1.0] + [0.0] * order

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


   def  __magic_name__				(					self     :							List[Any]			,			lowerCAmelCase_     :							list[float]			,			lowerCAmelCase_     :							list[float]     ):

      """simple docstring"""
      if len(lowerCAmelCase_     ) < self.order:
         _A:  int					=       [1.0, *a_coeffs]

      if len(lowerCAmelCase_     ) != self.order + 1:
         _A:  Union[str, Any]					=       (
             F"""Expected a_coeffs to have {self.order + 1} elements """
             F"""for {self.order}-order filter, got {len(lowerCAmelCase_     )}"""
         )
         raise ValueError(lowerCAmelCase_     )

      if len(lowerCAmelCase_     ) != self.order + 1:
         _A:  Any					=       (
             F"""Expected b_coeffs to have {self.order + 1} elements """
             F"""for {self.order}-order filter, got {len(lowerCAmelCase_     )}"""
         )
         raise ValueError(lowerCAmelCase_     )

      _A:  Tuple					=       a_coeffs
      _A:  Optional[int]					=       b_coeffs


   def  __magic_name__				(					self     :							Any			,			lowerCAmelCase_     :							float     ):

      """simple docstring"""
      _A:  str					=       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:  Tuple					=       (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

      _A:  Optional[Any]					=       self.input_history[:-1]
      _A:  Any					=       self.output_history[:-1]

      _A:  Union[str, Any]					=       sample
      _A:  Dict					=       result

      return result





from __future__ import annotations






class UpperCAmelCase   :





   '''simple docstring'''


   def __init__(					self     :							Optional[Any]			,			lowerCAmelCase_     :							int     ):

      """simple docstring"""
      _A:  List[str]					=       data
      _A:  Node | None					=       None
      _A:  Node | None					=       None






def   lowerCamelCase__							(					a      )      ->   None:  # In Order traversal of the tree
   if tree:
      display(tree.left      )
      print(tree.data      )
      display(tree.right      )






def   lowerCamelCase__							(					a      )      ->   int:
   return 1 + max(depth_of_tree(tree.left      )		,		depth_of_tree(tree.right      )      ) if tree else 0






def   lowerCamelCase__							(					a      )      ->   bool:
   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   lowerCamelCase__							(					)      ->   None:  # Main function for testing.
   _A:  Optional[int]					=       Node(1      )
   _A:  int					=       Node(2      )
   _A:  str					=       Node(3      )
   _A:  Union[str, Any]					=       Node(4      )
   _A:  Dict					=       Node(5      )
   _A:  int					=       Node(6      )
   _A:  Optional[Any]					=       Node(7      )
   _A:  List[str]					=       Node(8      )
   _A:  int					=       Node(9      )

   print(is_full_binary_tree(a      )      )
   print(depth_of_tree(a      )      )
   print('''Tree is: '''      )
   display(a      )


if __name__ == "__main__":
   main()



