






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





def 					lowercase_ (    __snake_case     :							List[str]	,	__snake_case     :							str	,	__snake_case     :							int = "x"	,	__snake_case     :							List[Any] = 1_0**-1_0	,	__snake_case     :							List[str] = 1	,	)     -> int:





				'''simple docstring'''


				snake_case__      :str         =   symbols(_lowerCamelCase      )
				snake_case__      :int         =   lambdify(_lowerCamelCase	,	_lowerCamelCase      )
				snake_case__      :List[str]         =   lambdify(_lowerCamelCase	,	diff(_lowerCamelCase	,	_lowerCamelCase      )      )

				snake_case__      :Optional[int]         =   starting_point

				while True:
								if diff_function(_lowerCamelCase      ) != 0:
												snake_case__      :Optional[Any]         =   prev_guess - multiplicity * func(_lowerCamelCase      ) / diff_function(
												    _lowerCamelCase      )
								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

								snake_case__      :int         =   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', 1_0, precision=0.005)}''',
	)

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







__UpperCAmelCase							:   int							=  {"a": ["c", "b"], "b": ["d", "e"], "c": [], "d": [], "e": []}
__UpperCAmelCase							:   List[str]							=  ["a", "b", "c", "d", "e"]





def 					lowercase_ (    __snake_case     :							Optional[Any]	,	__snake_case     :							List[Any]	,	__snake_case     :							Tuple      )     -> Optional[int]:





				'''simple docstring'''


				snake_case__      :List[Any]         =   start
				# add current to visited
				visited.append(__snake_case      )
				snake_case__      :List[str]         =   edges[current]
				for neighbor in neighbors:
								# if neighbor not in visited, visit
								if neighbor not in visited:
												snake_case__      :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:
																snake_case__      :Any         =   topological_sort(__snake_case	,	__snake_case	,	__snake_case      )
    # return sort
				return sort


if __name__ == "__main__":
	__UpperCAmelCase							:   Tuple							=  topological_sort("a", [], [])
	print(sort)