




"""simple docstring"""




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



def 					a__				(       snake_case__ ,				snake_case__ ,				snake_case__ = "x" ,				snake_case__ = 10**-10 ,				snake_case__ = 1 ,				)		->      complex:
			lowerCamelCase       =      symbols(__SCREAMING_SNAKE_CASE       )
			lowerCamelCase       =      lambdify(__SCREAMING_SNAKE_CASE ,				__SCREAMING_SNAKE_CASE       )
			lowerCamelCase       =      lambdify(__SCREAMING_SNAKE_CASE ,				diff(__SCREAMING_SNAKE_CASE ,				__SCREAMING_SNAKE_CASE       )       )

			lowerCamelCase       =      starting_point

			while True:
						if diff_function(__SCREAMING_SNAKE_CASE       ) != 0:
									lowerCamelCase       =      prev_guess - multiplicity * func(__SCREAMING_SNAKE_CASE       ) / diff_function(
									    __SCREAMING_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

						lowerCamelCase       =      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=0.0_0_5)}""",
					)

					# 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

lowerCAmelCase							:    str  							=							[-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
lowerCAmelCase							:    Dict  							=							[-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]



def 					a__				(       snake_case__       )		->      list[float]:
			lowerCamelCase       =      []
			lowerCamelCase       =      len(snake_case__       )

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



def 					a__				(       snake_case__       )		->      list[float]:
			lowerCamelCase       =      []
			for i, outer in enumerate(snake_case__       ):
						lowerCamelCase       =      -1
						for inner in arr[i + 1 :]:
									if outer < inner:
												lowerCamelCase       =      inner
												break
						result.append(snake_case__       )
			return result



def 					a__				(       snake_case__       )		->      list[float]:
			lowerCamelCase       =      len(snake_case__       )
			lowerCamelCase       =      []
			lowerCamelCase       =      [-1] * arr_size

			for index in reversed(range(snake_case__       )       ):
						if stack:
									while stack[-1] <= arr[index]:
												stack.pop()
												if not stack:
															break
						if stack:
									lowerCamelCase       =      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))

					lowerCAmelCase							:    Dict  							=							(
					    """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),
					)



