




import math




def 					lowerCamelCase__       (						A__       :					float  ,			A__       :					float	):





       '''simple docstring'''



       return math.pow(A__  ,			2	) - a




def 					lowerCamelCase__       (						A__       :					float	):





       '''simple docstring'''



       return 2 * x




def 					lowerCamelCase__       (						A__       :					float	):





       '''simple docstring'''



       __lowerCamelCase   =						2.0

       while start <= a:
              __lowerCamelCase   =						math.pow(A__  ,			2	)

       return start




def 					lowerCamelCase__       (						A__       :					float  ,			A__       :					int = 9999  ,			A__       :					float = 0.00_000_000_000_001	):





       '''simple docstring'''



       if a < 0:
              raise ValueError("""math domain error"""	)

       __lowerCamelCase   =						get_initial_point(A__	)

       for _ in range(A__	):
              __lowerCamelCase   =						value
              __lowerCamelCase   =						value - fx(A__  ,			A__	) / fx_derivative(A__	)
              if abs(prev_value - value	) < tolerance:
                     return value

       return value


if __name__ == "__main__":
       from doctest import testmod

       testmod()




def 			UpperCAmelCase__				(			_A      : dict							):





  '''simple docstring'''







  a__  =set()
  # To detect a back edge, keep track of vertices currently in the recursion stack
  a__  =set()
  return any(
      node not in visited and depth_first_search(_A	,      _A	,      _A	,      _A							)
      for node in graph							)




def 			UpperCAmelCase__				(			_A      : dict	,      _A      : int	,      _A      : set	,      _A      : set							):





  '''simple docstring'''







  visited.add(_A							)
  rec_stk.add(_A							)

  for node in graph[vertex]:
    if node not in visited:
      if depth_first_search(_A	,      _A	,      _A	,      _A							):
        return True
    elif node in rec_stk:
      return True

    # The node needs to be removed from recursion stack before function ends
  rec_stk.remove(_A							)
  return False


if __name__ == "__main__":
       from doctest import testmod

       testmod()
