





from __future__ import annotations

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

SCREAMING_SNAKE_CASE__       :			Tuple			      =						TypeVar("""T""")







class   __lowerCAmelCase			(					Generic[T]  ):





   def __init__( self					,			snake_case      )				->  Tuple:
      """simple docstring"""





      a__	:						Tuple      		=  data
      a__	:						Node[T] | None      		=  None





   def __str__( self      )				->  str:
      """simple docstring"""





      return F"""{self.data}"""







class   __lowerCAmelCase			(					Generic[T]  ):





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





      a__	:						Node[T] | None      		=  None





   def __iter__( self      )				->  Iterator[T]:
      """simple docstring"""





      a__	:						Tuple      		=  self.top
      while node:
         yield node.data
         a__	:						Optional[int]      		=  node.next





   def __str__( self      )				->  str:
      """simple docstring"""





      return "->".join([str(snake_case      ) for item in self]      )





   def __len__( self      )				->  int:
      """simple docstring"""





      return len(tuple(iter(self      )      )      )





   def 	_snake_case ( self      )				->  bool:
      """simple docstring"""





      return self.top is None





   def 	_snake_case ( self					,			snake_case      )				->  None:
      """simple docstring"""





      a__	:						Any      		=  Node(snake_case      )
      if not self.is_empty():
         a__	:						Optional[Any]      		=  self.top
      a__	:						List[str]      		=  node





   def 	_snake_case ( self      )				->  T:
      """simple docstring"""





      if self.is_empty():
         raise IndexError("pop from empty stack"      )
      assert isinstance(self.top					,			snake_case      )
      a__	:						Optional[Any]      		=  self.top
      a__	:						Optional[Any]      		=  self.top.next
      return pop_node.data





   def 	_snake_case ( 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 	_snake_case ( self      )				->  None:
      """simple docstring"""





      a__	:						Optional[int]      		=  None


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

  testmod()








from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean






def       _A  (      lowerCamelCase   ):

   # A local function to see if a dot lands in the circle.
   def is_in_circle(lowerCamelCase							, lowerCamelCase   ) -> bool:
      a__	:						Any      		=  sqrt((x**2) + (y**2)   )
      # Our circle has a radius of 1, so a distance
      # greater than 1 would land outside the circle.
      return distance_from_centre <= 1

   # The proportion of guesses that landed in the circle
   a__	:						Union[str, Any]      		=  mean(
       int(is_in_circle(uniform(-1.0							, 1.0   )							, uniform(-1.0							, 1.0   )   )   )
       for _ in range(lowerCamelCase   )   )
   # The ratio of the area for circle to square is pi/4.
   a__	:						Any      		=  proportion * 4
   print(F"""The estimated value of pi is {pi_estimate}"""   )
   print(F"""The numpy value of pi is {pi}"""   )
   print(F"""The total error is {abs(pi - pi_estimate   )}"""   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase = 0.0							, lowerCamelCase = 1.0							, ):
   return mean(
       function_to_integrate(uniform(lowerCamelCase							, lowerCamelCase   )   ) for _ in range(lowerCamelCase   )   ) * (max_value - min_value)






def       _A  (      lowerCamelCase							, lowerCamelCase = 0.0							, lowerCamelCase = 1.0   ):

   def identity_function(lowerCamelCase   ) -> float:
      return x

   a__	:						int      		=  area_under_curve_estimator(
       lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )
   a__	:						int      		=  (max_value * max_value - min_value * min_value) / 2

   print("******************"   )
   print(F"""Estimating area under y=x where x varies from {min_value} to {max_value}"""   )
   print(F"""Estimated value is {estimated_value}"""   )
   print(F"""Expected value is {expected_value}"""   )
   print(F"""Total error is {abs(estimated_value - expected_value   )}"""   )
   print("******************"   )






def       _A  (      lowerCamelCase   ):

   def function_to_integrate(lowerCamelCase   ) -> float:
      return sqrt(4.0 - x * x   )

   a__	:						int      		=  area_under_curve_estimator(
       lowerCamelCase							, lowerCamelCase							, 0.0							, 2.0   )

   print("******************"   )
   print("Estimating pi using area_under_curve_estimator"   )
   print(F"""Estimated value is {estimated_value}"""   )
   print(F"""Expected value is {pi}"""   )
   print(F"""Total error is {abs(estimated_value - pi   )}"""   )
   print("******************"   )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

