



from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
A__    :    int        =   10


def      UpperCamelCase(    __UpperCamelCase				:						int	,__UpperCamelCase				:						int	,__UpperCamelCase				:						list[int]	,__UpperCamelCase				:						int					):
		for i in range(a__	,a__					):
				if array[i] == target:
						return i
		return -1


def      UpperCamelCase(    __UpperCamelCase				:						list[int]	,__UpperCamelCase				:						int					):
		lowerCAmelCase_     :	Tuple							   =					0
		lowerCAmelCase_     :	Dict							   =					len(a__					)
		while left <= right:
				if right - left < precision:
						return lin_search(a__	,a__	,a__	,a__					)

				lowerCAmelCase_     :	Optional[Any]							   =					(left + right) // 3 + 1
				lowerCAmelCase_     :	Any							   =					2 * (left + right) // 3 + 1

				if array[one_third] == target:
						return one_third
				elif array[two_third] == target:
						return two_third

				elif target < array[one_third]:
						lowerCAmelCase_     :	Union[str, Any]							   =					one_third - 1
				elif array[two_third] < target:
						lowerCAmelCase_     :	List[Any]							   =					two_third + 1

				else:
						lowerCAmelCase_     :	List[Any]							   =					one_third + 1
						lowerCAmelCase_     :	int							   =					two_third - 1
		else:
				return -1


def      UpperCamelCase(    __UpperCamelCase				:						int	,__UpperCamelCase				:						int	,__UpperCamelCase				:						list[int]	,__UpperCamelCase				:						int					):
		if left < right:
				if right - left < precision:
						return lin_search(a__	,a__	,a__	,a__					)
				lowerCAmelCase_     :	Optional[Any]							   =					(left + right) // 3 + 1
				lowerCAmelCase_     :	List[str]							   =					2 * (left + right) // 3 + 1

				if array[one_third] == target:
						return one_third
				elif array[two_third] == target:
						return two_third

				elif target < array[one_third]:
						return rec_ternary_search(a__	,one_third - 1	,a__	,a__					)
				elif array[two_third] < target:
						return rec_ternary_search(two_third + 1	,a__	,a__	,a__					)
				else:
						return rec_ternary_search(one_third + 1	,two_third - 1	,a__	,a__					)
		else:
				return -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						A__    :    Any        =   input('''Enter numbers separated by comma:\n''').strip()
						A__    :    List[str]        =   [int(item.strip()) for item in user_input.split(''',''')]
						assert collection == sorted(collection), F"List must be ordered.\n{collection}."
						A__    :    Optional[int]        =   int(input('''Enter the number to be found in the list:\n''').strip())
						A__    :    List[Any]        =   ite_ternary_search(collection, target)
						A__    :    Optional[int]        =   rec_ternary_search(0, len(collection) - 1, collection, target)
						if resulta != -1:
												print(F'''Iterative search: {target} found at positions: {resulta}''')
												print(F'''Recursive search: {target} found at positions: {resulta}''')
						else:
												print('''Not found''')








from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str			,a__    :   complex			,a__    :   str = "x"			,a__    :   float = 10**-10			,a__    :   int = 1			,)					->				complex:
	__A :			Tuple		    =			symbols(a__       )
	__A :			List[str]		    =			lambdify(a__			,a__       )
	__A :			Any		    =			lambdify(a__			,diff(a__			,a__       )       )

	__A :			Dict		    =			starting_point

	while True:
		if diff_function(a__       ) != 0:
			__A :			Optional[int]		    =			prev_guess - multiplicity * func(a__       ) / diff_function(
			    a__       )
		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 :			List[Any]		    =			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)}""")





