



"""simple docstring"""

from copy import deepcopy




class        _UpperCAmelCase       :

 def __init__(     self		:       List[str]  ,     lowercase_		:       list[int] | None = None  ,     lowercase_		:       int | None = None				):

     if arr is None and size is not None:
         snake_case_ :     Dict				=	size
         snake_case_ :     List[Any]				=	[0] * size
     elif arr is not None:
         self.init(lowercase_				)
     else:
         raise ValueError('''Either arr or size must be specified'''				)

 def 						_snake_case					(     self		:       Dict  ,     lowercase_		:       list[int]				):
     snake_case_ :     Union[str, Any]				=	len(lowercase_				)
     snake_case_ :     Tuple				=	deepcopy(lowercase_				)
     for i in range(1  ,     self.size				):
         snake_case_ :     Tuple				=	self.next_(lowercase_				)
         if j < self.size:
             self.tree[j] += self.tree[i]

 def 						_snake_case					(     self		:       Union[str, Any]				):
     snake_case_ :     Optional[int]				=	self.tree[:]
     for i in range(self.size - 1  ,     0  ,     -1				):
         snake_case_ :     List[Any]				=	self.next_(lowercase_				)
         if j < self.size:
             arr[j] -= arr[i]
     return arr

 @staticmethod
 def 						_snake_case					(     lowercase_		:       int				):
     return index + (index & (-index))

 @staticmethod
 def 						_snake_case					(     lowercase_		:       int				):
     return index - (index & (-index))

 def 						_snake_case					(     self		:       Dict  ,     lowercase_		:       int  ,     lowercase_		:       int				):
     if index == 0:
         self.tree[0] += value
         return
     while index < self.size:
         self.tree[index] += value
         snake_case_ :     Any				=	self.next_(lowercase_				)

 def 						_snake_case					(     self		:       Tuple  ,     lowercase_		:       int  ,     lowercase_		:       int				):
     self.add(lowercase_  ,     value - self.get(lowercase_				)				)

 def 						_snake_case					(     self		:       Dict  ,     lowercase_		:       int				):
     if right == 0:
         return 0
     snake_case_ :     Optional[int]				=	self.tree[0]
     right -= 1  # make right inclusive
     while right > 0:
         result += self.tree[right]
         snake_case_ :     Union[str, Any]				=	self.prev(lowercase_				)
     return result

 def 						_snake_case					(     self		:       List[Any]  ,     lowercase_		:       int  ,     lowercase_		:       int				):
     return self.prefix(lowercase_				) - self.prefix(lowercase_				)

 def 						_snake_case					(     self		:       List[str]  ,     lowercase_		:       int				):
     return self.query(lowercase_  ,     index + 1				)






 def 						_snake_case					(     self		:       Optional[int]  ,     lowercase_		:       int				):
     value -= self.tree[0]
     if value < 0:
         return -1

     snake_case_ :     Optional[int]				=	1  # Largest power of 2 <= size
     while j * 2 < self.size:
         j *= 2

     snake_case_ :     Tuple				=	0

     while j > 0:
         if i + j < self.size and self.tree[i + j] <= value:
             value -= self.tree[i + j]
             i += j
         j //= 2
     return i


if __name__ == "__main__":
     import doctest

     doctest.testmod()










"""simple docstring"""

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




def __lowercase			(							_a		,			_a		,			_a = "x"		,			_a = 10**-10		,			_a = 1		,			):
    snake_case_ :     Any				=	symbols(_a    )
    snake_case_ :     int				=	lambdify(_a		,			_a    )
    snake_case_ :     Optional[Any]				=	lambdify(_a		,			diff(_a		,			_a    )    )

    snake_case_ :     Optional[Any]				=	starting_point

    while True:
        if diff_function(_a    ) != 0:
            snake_case_ :     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

        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", 10, precision=0.005)}',
     )

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





