



"""simple docstring"""


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







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



				def is_in_circle(_SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				) -> bool:
								_UpperCAmelCase					=    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
				_UpperCAmelCase					=    mean(
				    int(is_in_circle(uniform(-1.0					,     1.0				)					,     uniform(-1.0					,     1.0				)				)				)
				    for _ in range(_SCREAMING_SNAKE_CASE				)				)
				# The ratio of the area for circle to square is pi/4.
				_UpperCAmelCase					=    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  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						Callable[[float], float]					,     _SCREAMING_SNAKE_CASE   :						float = 0.0					,     _SCREAMING_SNAKE_CASE   :						float = 1.0					,     ):






				'''simple docstring'''



				return mean(
				    function_to_integrate(uniform(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)				) for _ in range(_SCREAMING_SNAKE_CASE				)				) * (max_value - min_value)







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						float = 0.0					,     _SCREAMING_SNAKE_CASE   :						float = 1.0				):






				'''simple docstring'''



				def identity_function(_SCREAMING_SNAKE_CASE   :						float				) -> float:
								return x

				_UpperCAmelCase					=    area_under_curve_estimator(
				    _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)
				_UpperCAmelCase					=    (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  lowercase	(      _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



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

				_UpperCAmelCase					=    area_under_curve_estimator(
				    _SCREAMING_SNAKE_CASE					,     _SCREAMING_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()








"""simple docstring"""


import operator







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						list					,     _SCREAMING_SNAKE_CASE   :						bool = False					,     _SCREAMING_SNAKE_CASE   :						list | None = None				):






				'''simple docstring'''



				_UpperCAmelCase					=    operator.lt if reverse else operator.gt
				_UpperCAmelCase					=    solution or []

				if not arr:
								return solution

				_UpperCAmelCase					=    [arr.pop(0				)]
				for i, item in enumerate(_SCREAMING_SNAKE_CASE				):
								if _operator(_SCREAMING_SNAKE_CASE					,     sublist[-1]				):
												sublist.append(_SCREAMING_SNAKE_CASE				)
												arr.pop(_SCREAMING_SNAKE_CASE				)

    #  merging sublist into solution list
				if not solution:
								solution.extend(_SCREAMING_SNAKE_CASE				)
				else:
								while sublist:
												_UpperCAmelCase					=    sublist.pop(0				)
												for i, xx in enumerate(_SCREAMING_SNAKE_CASE				):
																if not _operator(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				):
																				solution.insert(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)
																				break
												else:
																solution.append(_SCREAMING_SNAKE_CASE				)

				strand_sort(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)
				return solution


if __name__ == "__main__":
					assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
					assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]



