


'''simple docstring'''






from __future__ import annotations




class  a     :
 def __init__( self      ,				__magic_name__						)					->							None:
      _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 							__UpperCAmelCase		( self      ,				__magic_name__      ,				__magic_name__						)					->							None:
      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 							__UpperCAmelCase		( self      ,				__magic_name__						)					->							float:
      _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





'''simple docstring'''






def 	_A				(lowerCAmelCase__  :Union[str, Any]		)   ->  List[str]:




     '''simple docstring'''



     return [
         {
             0: [1, 2],
             1: [0, 2],
             2: [0, 1, 3, 5],
             3: [2, 4],
             4: [3],
             5: [2, 6, 8],
             6: [5, 7],
             7: [6, 8],
             8: [5, 7],
         },
         {
             0: [6],
             1: [9],
             2: [4, 5],
             3: [4],
             4: [2, 3],
             5: [2],
             6: [0, 7],
             7: [6],
             8: [],
             9: [1],
         },
         {
             0: [4],
             1: [6],
             2: [],
             3: [5, 6, 7],
             4: [0, 6],
             5: [3, 8, 9],
             6: [1, 3, 4, 7],
             7: [3, 6, 8, 9],
             8: [5, 7],
             9: [5, 7],
         },
         {
             0: [1, 3],
             1: [0, 2, 4],
             2: [1, 3, 4],
             3: [0, 2, 4],
             4: [1, 2, 3],
         },
     ][index]






def 	_A				(lowerCAmelCase__  :dict[int, list[int]]		)   ->  list[tuple[int, int]]:




     '''simple docstring'''



     _a			      =							0
     _a			      =							len(lowerCAmelCase__		)  # No of vertices in graph
     _a			      =							[0] * n
     _a			      =							[False] * n

     def dfs(lowerCAmelCase__  :Dict				,						lowerCAmelCase__  :str				,						lowerCAmelCase__  :Dict				,						lowerCAmelCase__  :Union[str, Any]		):
          _a			      =							True
          _a			      =							id_
          id_ += 1
          for to in graph[at]:
               if to == parent:
                    pass
               elif not visited[to]:
                    dfs(lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__				,						id_		)
                    _a			      =							min(low[at]				,						low[to]		)
                    if id_ <= low[to]:
                         bridges.append((at, to) if at < to else (to, at)		)
               else:
                    # This edge is a back edge and cannot be a bridge
                    _a			      =							min(low[at]				,						low[to]		)

     _a			      =							[]
     for i in range(lowerCAmelCase__		):
          if not visited[i]:
               dfs(lowerCAmelCase__				,						-1				,						lowerCAmelCase__				,						id_		)
     return bridges


if __name__ == "__main__":
 import doctest

 doctest.testmod()

