
'''simple docstring'''




from math import factorial







def 		lowerCAmelCase_				(   snake_case__		,				snake_case__		,				snake_case__						):




    '''simple docstring'''



    if successes > trials:
        raise ValueError('''successes must be lower or equal to trials'''						)
    if trials < 0 or successes < 0:
        raise ValueError('''the function is defined for non-negative integers'''						)
    if not isinstance(snake_case__		,				snake_case__						) or not isinstance(snake_case__		,				snake_case__						):
        raise ValueError('''the function is defined for non-negative integers'''						)
    if not 0 < prob < 1:
        raise ValueError('''prob has to be in range of 1 - 0'''						)
    A       :   Any					=						(prob**successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    A       :   Tuple					=						float(factorial(snake_case__						)						)
    coefficient /= factorial(snake_case__						) * factorial(trials - successes						)
    return probability * coefficient


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

      testmod()
      print('Probability of 2 successes out of 4 trails')
      print('with probability of 0.75 is:', end=' ')
      print(binomial_distribution(2, 4, 0.75))









'''simple docstring'''




class 	_lowerCAmelCase							(			__UpperCAmelCase ):
	pass







class 	_lowerCAmelCase							(			__UpperCAmelCase ):
	pass







class 	_lowerCAmelCase							:


	def __init__(self							):
				A_	:						List[Any]	=     [
				    [],
				    [],
				    [],
				]


	def     _a	(self       ,      lowercase       ,      lowercase							):
				try:
							if len(self.queues[priority]							) >= 100:
										raise OverflowError("""Maximum queue size is 100"""							)
							self.queues[priority].append(lowercase							)
				except IndexError:
							raise ValueError("""Valid priorities are 0, 1, and 2"""							)


	def     _a	(self							):
				for queue in self.queues:
							if queue:
										return queue.pop(0							)
				raise UnderFlowError("""All queues are empty"""							)


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







class 	_lowerCAmelCase							:


	def __init__(self							):
				A_	:						List[str]	=     []


	def     _a	(self       ,      lowercase							):
				if len(self.queue							) == 100:
							raise OverFlowError("""Maximum queue size is 100"""							)
				self.queue.append(lowercase							)


	def     _a	(self							):
				if not self.queue:
							raise UnderFlowError("""The queue is empty"""							)
				else:
							A_	:						List[Any]	=     min(self.queue							)
							self.queue.remove(lowercase							)
							return data


	def __str__(self							):
				return str(self.queue							)






def 	a			( ):
			'''simple docstring'''





			A_	:						Optional[int]	=     FixedPriorityQueue()
			fpq.enqueue(0						,      10    )
			fpq.enqueue(1						,      70    )
			fpq.enqueue(0						,      1_00    )
			fpq.enqueue(2						,      1    )
			fpq.enqueue(2						,      5    )
			fpq.enqueue(1						,      7    )
			fpq.enqueue(2						,      4    )
			fpq.enqueue(1						,      64    )
			fpq.enqueue(0						,      1_28    )
			print(lowerCamelCase__    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(lowerCamelCase__    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )
			print(fpq.dequeue()    )



def 	a			( ):
			'''simple docstring'''





			A_	:						int	=     ElementPriorityQueue()
			epq.enqueue(10    )
			epq.enqueue(70    )
			epq.enqueue(1_00    )
			epq.enqueue(1    )
			epq.enqueue(5    )
			epq.enqueue(7    )
			epq.enqueue(4    )
			epq.enqueue(64    )
			epq.enqueue(1_28    )
			print(lowerCamelCase__    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(lowerCamelCase__    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )
			print(epq.dequeue()    )


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