




from __future__ import annotations







def        lowerCAmelCase_			(  snake_case_  ):
      if len(snake_case_  ) == 0:
            return array

      _A    ,     _A							:  Tuple    =		min(snake_case_  ), max(snake_case_  )

      # Compute the variables
      _A							:  Tuple    =		_max - _min + 1
      _A    ,     _A							:  str    =		[0] * holes_range, [0] * holes_range

      # Make the sorting.
      for i in array:
            _A							:  Union[str, Any]    =		i - _min
            _A							:  List[str]    =		i
            holes_repeat[index] += 1

      # Makes the array back by replacing the numbers.
      _A							:  Tuple    =		0
      for i in range(snake_case_  ):
            while holes_repeat[i] > 0:
                  _A							:  Union[str, Any]    =		holes[i]
                  index += 1
                  holes_repeat[i] -= 1

    # Returns the sorted array.
      return array


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  _snake_case            = input("Enter numbers separated by comma:\n")
  _snake_case            = [int(x) for x in user_input.split(",")]
  print(pigeon_sort(unsorted))







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







def        lowerCAmelCase_			(  snake_case_  ):

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







def        lowerCAmelCase_			(  snake_case_,snake_case_ = 0.0,snake_case_ = 1.0  ):

      def identity_function(snake_case_  ) -> float:
            return x

      _A							:  Any    =		area_under_curve_estimator(
          snake_case_,snake_case_,snake_case_,snake_case_  )
      _A							:  Tuple    =		(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        lowerCAmelCase_			(  snake_case_  ):

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

      _A							:  Optional[int]    =		area_under_curve_estimator(
          snake_case_,snake_case_,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()

