



"""simple docstring"""


class 			_a (					lowerCAmelCase):
			"""simple docstring"""
			pass



class 			_a (					lowerCAmelCase):
			"""simple docstring"""
			pass



class 			_a :
			"""simple docstring"""



			def __init__(		self     :    Optional[Any]   )->Tuple:
							_UpperCAmelCase					=    [
							    [],
							    [],
							    [],
							]



			def  lowercase__						(		self     :    Optional[Any]				,   __UpperCamelCase     :    int				,   __UpperCamelCase     :    int   )->None:
							try:
											if len(self.queues[priority]   ) >= 1_0_0:
															raise OverflowError('''Maximum queue size is 100'''   )
											self.queues[priority].append(__UpperCamelCase   )
							except IndexError:
											raise ValueError('''Valid priorities are 0, 1, and 2'''   )



			def  lowercase__						(		self     :    int   )->int:
							for queue in self.queues:
											if queue:
															return queue.pop(0   )
							raise UnderFlowError('''All queues are empty'''   )



			def __str__(		self     :    str   )->str:
							return "\n".join(F'Priority {i}: {q}' for i, q in enumerate(self.queues   )   )



class 			_a :
			"""simple docstring"""



			def __init__(		self     :    Union[str, Any]   )->Optional[Any]:
							_UpperCAmelCase					=    []



			def  lowercase__						(		self     :    str				,   __UpperCamelCase     :    int   )->None:
							if len(self.queue   ) == 1_0_0:
											raise OverFlowError('''Maximum queue size is 100'''   )
							self.queue.append(__UpperCamelCase   )



			def  lowercase__						(		self     :    Dict   )->int:
							if not self.queue:
											raise UnderFlowError('''The queue is empty'''   )
							else:
											_UpperCAmelCase					=    min(self.queue   )
											self.queue.remove(__UpperCamelCase   )
											return data



			def __str__(		self     :    Optional[Any]   )->str:
							return str(self.queue   )







def  lowercase	(      ):






				'''simple docstring'''



				_UpperCAmelCase					=    FixedPriorityQueue()
				fpq.enqueue(0					,     10				)
				fpq.enqueue(1					,     70				)
				fpq.enqueue(0					,     100				)
				fpq.enqueue(2					,     1				)
				fpq.enqueue(2					,     5				)
				fpq.enqueue(1					,     7				)
				fpq.enqueue(2					,     4				)
				fpq.enqueue(1					,     64				)
				fpq.enqueue(0					,     128				)
				print(_SCREAMING_SNAKE_CASE				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(_SCREAMING_SNAKE_CASE				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)
				print(fpq.dequeue()				)







def  lowercase	(      ):






				'''simple docstring'''



				_UpperCAmelCase					=    ElementPriorityQueue()
				epq.enqueue(10				)
				epq.enqueue(70				)
				epq.enqueue(100				)
				epq.enqueue(1				)
				epq.enqueue(5				)
				epq.enqueue(7				)
				epq.enqueue(4				)
				epq.enqueue(64				)
				epq.enqueue(128				)
				print(_SCREAMING_SNAKE_CASE				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(_SCREAMING_SNAKE_CASE				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)
				print(epq.dequeue()				)


if __name__ == "__main__":
					fixed_priority_queue()
					element_priority_queue()








"""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()



