


from __future__ import annotations




def 	__lowercase		(  _UpperCamelCase   )			->None:







      """simple docstring"""

      create_state_space_tree(__snake_case,			[],			0,			[0 for i in range(len(__snake_case   )   )]   )




def 	__lowercase		(  _UpperCamelCase,			_UpperCamelCase,			_UpperCamelCase,			_UpperCamelCase,			)			->None:







      """simple docstring"""

      if index == len(__snake_case   ):
            print(__snake_case   )
            return

      for i in range(len(__snake_case   )   ):
            if not index_used[i]:
                  current_sequence.append(sequence[i]   )
                  lowercase	:      Dict          =						True
                  create_state_space_tree(__snake_case,			__snake_case,			index + 1,			__snake_case   )
                  current_sequence.pop()
                  lowercase	:      int          =						False
__a       =					[3, 1, 2, 4]
generate_all_permutations(sequence)

__a       =					["A", "B", "C"]



generate_all_permutations(sequence_a)








'''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)}""")