
from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

_UpperCAmelCase      :				Union[str, Any]          = TypeVar("T")


class        lowercase      (	Generic[T]     ):



		def __init__(				self       ,   A_ )						->      Dict:
				"""simple docstring"""
				UpperCamelCase						=  data
				UpperCamelCase						=  None



		def __str__(				self )						->      str:
				"""simple docstring"""
				return F'''{self.data}'''






class        lowercase      (	Generic[T]     ):



		def __init__(				self )						->      None:
				"""simple docstring"""
				UpperCamelCase						=  None



		def __iter__(				self )						->      Iterator[T]:
				"""simple docstring"""
				UpperCamelCase						=  self.top
				while node:
						yield node.data
						UpperCamelCase						=  node.next



		def __str__(				self )						->      str:
				"""simple docstring"""
				return "->".join([str(A_ ) for item in self] )



		def __len__(				self )						->      int:
				"""simple docstring"""
				return len(tuple(iter(self ) ) )



		def __UpperCamelCase				(				self )						->      bool:
				"""simple docstring"""
				return self.top is None



		def __UpperCamelCase				(				self       ,   A_ )						->      None:
				"""simple docstring"""
				UpperCamelCase						=  Node(A_ )
				if not self.is_empty():
						UpperCamelCase						=  self.top
				UpperCamelCase						=  node



		def __UpperCamelCase				(				self )						->      T:
				"""simple docstring"""
				if self.is_empty():
						raise IndexError('pop from empty stack' )
				assert isinstance(self.top       ,   A_ )
				UpperCamelCase						=  self.top
				UpperCamelCase						=  self.top.next
				return pop_node.data



		def __UpperCamelCase				(				self )						->      T:
				"""simple docstring"""
				if self.is_empty():
						raise IndexError('peek from empty stack' )

				assert self.top is not None
				return self.top.data



		def __UpperCamelCase				(				self )						->      None:
				"""simple docstring"""
				UpperCamelCase						=  None


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

					testmod()


from collections.abc import Callable


def    A (      lowercase					, lowercase					, lowercase				)     ->						float:
		'''simple docstring'''

		UpperCamelCase						=  a
		UpperCamelCase						=  b
		if function(lowercase				) == 0:  # one of the a or b is a root for the function
				return a
		elif function(lowercase				) == 0:
				return b
		elif (
		    function(lowercase				) * function(lowercase				) > 0
		):  # if none of these are root and they are both positive or negative,
				# then this algorithm can't find the root
				raise ValueError('could not find root in given interval.'				)
		else:
				UpperCamelCase						=  start + (end - start) / 2.0
				while abs(start - mid				) > 10**-7:  # until precisely equals to 10^-7
						if function(lowercase				) == 0:
								return mid
						elif function(lowercase				) * function(lowercase				) < 0:
								UpperCamelCase						=  mid
						else:
								UpperCamelCase						=  mid
						UpperCamelCase						=  start + (end - start) / 2.0
				return mid


def    A (      lowercase				)     ->						float:
		'''simple docstring'''

		return x**3 - 2 * x - 5


if __name__ == "__main__":
					print(bisection(f, 1, 1_000))

					import doctest

					doctest.testmod()
