






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




def 				A		(					lowercase__  :  str ,		lowercase__  :  complex ,		lowercase__  :  str = "x" ,		lowercase__  :  float = 10**-10 ,		lowercase__  :  int = 1 ,		)		-> complex:
	UpperCamelCase__ :Optional[int]						=      symbols(lowercase__  )
	UpperCamelCase__ :Dict						=      lambdify(lowercase__ ,		lowercase__  )
	UpperCamelCase__ :Any						=      lambdify(lowercase__ ,		diff(lowercase__ ,		lowercase__  )  )

	UpperCamelCase__ :List[str]						=      starting_point

	while True:
		if diff_function(lowercase__  ) != 0:
			UpperCamelCase__ :List[Any]						=      prev_guess - multiplicity * func(lowercase__  ) / diff_function(
			    lowercase__  )
		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

		UpperCamelCase__ :Optional[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)}''')

"""simple docstring"""

from __future__ import annotations

SCREAMING_SNAKE_CASE_            =    [-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
SCREAMING_SNAKE_CASE_            =    [-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]




def      lowercase__    (       lowerCAmelCase					:       list[float]			)			->   list[float]:






    """simple docstring"""




    UpperCAmelCase          =       []
    UpperCAmelCase          =       len(lowerCAmelCase			)

    for i in range(lowerCAmelCase			):
        UpperCAmelCase          =       -1
        for j in range(i + 1			,					lowerCAmelCase			):
            if arr[i] < arr[j]:
                UpperCAmelCase          =       arr[j]
                break
        result.append(lowerCAmelCase			)
    return result




def      lowercase__    (       lowerCAmelCase					:       list[float]			)			->   list[float]:






    """simple docstring"""




    UpperCAmelCase          =       []
    for i, outer in enumerate(lowerCAmelCase			):
        UpperCAmelCase          =       -1
        for inner in arr[i + 1 :]:
            if outer < inner:
                UpperCAmelCase          =       inner
                break
        result.append(lowerCAmelCase			)
    return result




def      lowercase__    (       lowerCAmelCase					:       list[float]			)			->   list[float]:






    """simple docstring"""




    UpperCAmelCase          =       len(lowerCAmelCase			)
    UpperCAmelCase          =       []
    UpperCAmelCase          =       [-1] * arr_size

    for index in reversed(range(lowerCAmelCase			)			):
        if stack:
            while stack[-1] <= arr[index]:
                stack.pop()
                if not stack:
                    break
        if stack:
            UpperCAmelCase          =       stack[-1]
        stack.append(arr[index]			)
    return result


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

   testmod()
   print(next_greatest_element_slow(arr))
   print(next_greatest_element_fast(arr))
   print(next_greatest_element(arr))

   SCREAMING_SNAKE_CASE_            =    (
       '''from __main__ import arr, next_greatest_element_slow, '''
       '''next_greatest_element_fast, next_greatest_element'''
   )
   print(
       '''next_greatest_element_slow():''',
       timeit('''next_greatest_element_slow(arr)''', setup=setup),
   )
   print(
       '''next_greatest_element_fast():''',
       timeit('''next_greatest_element_fast(arr)''', setup=setup),
   )
   print(
       '''     next_greatest_element():''',
       timeit('''next_greatest_element(arr)''', setup=setup),
   )



