


"""simple docstring"""





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


def      _snake_case						(						_snake_case				:			List[str]			):

      # A local function to see if a dot lands in the circle.
      def is_in_circle(_snake_case				:			int ,   _snake_case				:			List[Any]			) -> bool:
            lowerCAmelCase					:	str       =   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
      lowerCAmelCase					:	Tuple       =   mean(
          int(is_in_circle(uniform(-1.0 ,   1.0			) ,   uniform(-1.0 ,   1.0			)			)			)
          for _ in range(lowercase__			)			)
      # The ratio of the area for circle to square is pi/4.
      lowerCAmelCase					:	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      _snake_case						(						_snake_case				:			Tuple ,   _snake_case				:			List[str] ,   _snake_case				:			str = 0.0 ,   _snake_case				:			Tuple = 1.0 ,   ):
      return mean(
          function_to_integrate(uniform(lowercase__ ,   lowercase__			)			) for _ in range(lowercase__			)			) * (max_value - min_value)


def      _snake_case						(						_snake_case				:			int ,   _snake_case				:			List[Any] = 0.0 ,   _snake_case				:			List[str] = 1.0			):

      def identity_function(_snake_case				:			str			) -> float:
            return x

      lowerCAmelCase					:	Any       =   area_under_curve_estimator(
          lowercase__ ,   lowercase__ ,   lowercase__ ,   lowercase__			)
      lowerCAmelCase					:	Any       =   (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      _snake_case						(						_snake_case				:			List[str]			):

      def function_to_integrate(_snake_case				:			Optional[Any]			) -> float:
            return sqrt(4.0 - x * x			)

      lowerCAmelCase					:	Optional[Any]       =   area_under_curve_estimator(
          lowercase__ ,   lowercase__ ,   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()









"""simple docstring"""





from __future__ import annotations

from typing import Any



class 		snake_case_(       a__			):
     pass



class 		snake_case_:






     def __init__(	self  :					Any					,				UpperCamelCase_  :					Any				):
           lowerCAmelCase					:	Any       =   data
           lowerCAmelCase					:	Node | None       =   None






     def __iter__(	self  :					int				):
           lowerCAmelCase					:	Any       =   self
           lowerCAmelCase					:	Union[str, Any]       =   []
           while node:
                 if node in visited:
                       raise ContainsLoopError
                 visited.append(UpperCamelCase_				)
                 yield node.data
                 lowerCAmelCase					:	Optional[int]       =   node.next_node






     @property
     def      lowerCamelCase__     (	self  :					str				):
           try:
                 list(self				)
                 return False
           except ContainsLoopError:
                 return True


if __name__ == "__main__":
 snake_case__		:     Dict    				=				Node(1)
 snake_case__		:     Any    				=				Node(2)
 snake_case__		:     int    				=				Node(3)
 snake_case__		:     Any    				=				Node(4)
 print(root_node.has_loop)  # False
 snake_case__		:     Tuple    				=				root_node.next_node
 print(root_node.has_loop)  # True

 snake_case__		:     List[Any]    				=				Node(5)
 snake_case__		:     int    				=				Node(6)
 snake_case__		:     List[Any]    				=				Node(5)
 snake_case__		:     Dict    				=				Node(6)
 print(root_node.has_loop)  # False

 snake_case__		:     Any    				=				Node(1)
 print(root_node.has_loop)  # False


