





'''simple docstring'''




lowercase__    :      Union[str, Any]						=    {'''a''': ['''c''', '''b'''], '''b''': ['''d''', '''e'''], '''c''': [], '''d''': [], '''e''': []}
lowercase__    :      int						=    ['''a''', '''b''', '''c''', '''d''', '''e''']






def        _lowerCAmelCase			(  __snake_case  : List[str] ,							__snake_case  : List[Any] ,							__snake_case  : Dict			)     ->     Tuple:
     __A						: List[Any]      =       start
     # add current to visited
     visited.append(__snake_case			)
     __A						: str      =       edges[current]
     for neighbor in neighbors:
          # if neighbor not in visited, visit
          if neighbor not in visited:
               __A						: Optional[Any]      =       topological_sort(__snake_case ,							__snake_case ,							__snake_case			)
    # if all neighbors visited add current to sort
     sort.append(__snake_case			)
     # if all vertices haven't been visited select a new one to visit
     if len(__snake_case			) != len(__snake_case			):
          for vertice in vertices:
               if vertice not in visited:
                    __A						: Optional[Any]      =       topological_sort(__snake_case ,							__snake_case ,							__snake_case			)
    # return sort
     return sort


if __name__ == "__main__":
  lowercase__    :      Optional[Any]						=    topological_sort('''a''', [], [])
  print(sort)






'''simple docstring'''




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        _lowerCAmelCase			(  __snake_case  : str ,							__snake_case  : complex ,							__snake_case  : str = "x" ,							__snake_case  : float = 10**-10 ,							__snake_case  : int = 1 ,							)     ->     complex:
     __A						: int      =       symbols(__snake_case			)
     __A						: Tuple      =       lambdify(__snake_case ,							__snake_case			)
     __A						: Any      =       lambdify(__snake_case ,							diff(__snake_case ,							__snake_case			)			)

     __A						: str      =       starting_point

     while True:
          if diff_function(__snake_case			) != 0:
               __A						: Optional[Any]      =       prev_guess - multiplicity * func(__snake_case			) / diff_function(
                   __snake_case			)
          else:
               raise ZeroDivisionError('Could not find root'			) from None

          # Precision is checked by comparing the difference of consecutive guesses
          if abs(next_guess - prev_guess			) < precision:
               return next_guess

          __A						: Dict      =       next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")

  # Find root of polynomial
  # Find fourth Root of 5
  print(f"""The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}""")

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      f"""{newton_raphson("log(y) - 1", 2, variable="y")}""",
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      f"""{newton_raphson("exp(x) - 1", 10, precision=0.005)}""",
  )

  # Find root of cos(x)
  print(f"""The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}""")