





class SCREAMING_SNAKE_CASE_    :






						def __init__(   self   :   str						)				->     Dict:







							"""simple docstring"""


							snake_case_		:      int           =						[0]
							snake_case_		:      List[Any]           =						0






						def UpperCAmelCase_					(   self   :   int		, _A   :   int						)				->     None:







							"""simple docstring"""


							snake_case_		:      Dict           =						self.__heap[i]
							while i // 2 > 0:
								if self.__heap[i] > self.__heap[i // 2]:
									snake_case_		:      List[Any]           =						self.__heap[i // 2]
									snake_case_		:      List[Any]           =						temporary
								i //= 2






						def UpperCAmelCase_					(   self   :   Optional[Any]		, _A   :   int						)				->     None:







							"""simple docstring"""


							self.__heap.append(_A						)
							self.__size += 1
							self.__swap_up(self.__size						)






						def UpperCAmelCase_					(   self   :   Any		, _A   :   int						)				->     None:







							"""simple docstring"""


							while self.__size >= 2 * i:
								if 2 * i + 1 > self.__size:
									snake_case_		:      str           =						2 * i
								else:
									if self.__heap[2 * i] > self.__heap[2 * i + 1]:
										snake_case_		:      Dict           =						2 * i
									else:
										snake_case_		:      int           =						2 * i + 1
								snake_case_		:      Optional[Any]           =						self.__heap[i]
								if self.__heap[i] < self.__heap[bigger_child]:
									snake_case_		:      int           =						self.__heap[bigger_child]
									snake_case_		:      Optional[int]           =						temporary
								snake_case_		:      Tuple           =						bigger_child






						def UpperCAmelCase_					(   self   :   int						)				->     int:







							"""simple docstring"""


							snake_case_		:      List[Any]           =						self.__heap[1]
							snake_case_		:      List[str]           =						self.__heap[self.__size]
							self.__size -= 1
							self.__heap.pop()
							self.__swap_down(1						)
							return max_value






						@property
						def UpperCAmelCase_					(   self   :   str						)				->     List[str]:







							"""simple docstring"""


							return self.__heap[1:]






						def __len__(   self   :   List[str]						)				->     Dict:







							"""simple docstring"""


							return self.__size


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						# create an instance of BinaryHeap
						_SCREAMING_SNAKE_CASE   						=		BinaryHeap()
						binary_heap.insert(6)
						binary_heap.insert(10)
						binary_heap.insert(15)
						binary_heap.insert(12)
						# pop root(max-values because it is max heap)
						print(binary_heap.pop())  # 15
						print(binary_heap.pop())  # 12
						# get the list and size after operations
						print(binary_heap.get_list)
						print(len(binary_heap))





_A		:					Union[str, Any]          =							1_000



def      __lowerCAmelCase    (				snake_case						:     float			)							->				float:
   return x * x



def      __lowerCAmelCase    (				snake_case						:     Optional[int]    ,   snake_case						:     float    ,   snake_case						:     float    ,   snake_case						:     int = 4			)							->				float:
   assert callable(
       snake_case			), f'the function(object) passed should be callable your input : {function}'
   assert isinstance(snake_case    ,   (float, int)			), f'a should be float or integer your input : {a}'
   assert isinstance(function(snake_case			)    ,   (float, int)			), (
       "the function should return integer or float return type of your function, "
       f'{type(snake_case			)}'
   )
   assert isinstance(snake_case    ,   (float, int)			), f'b should be float or integer your input : {b}'
   assert (
       isinstance(snake_case    ,   snake_case			) and precision > 0
   ), f'precision should be positive integer your input : {precision}'

   # just applying the formula of simpson for approximate integration written in
   # mentioned article in first comment of this file and above this function

   __lowerCamelCase:					List[str]	 =						(b - a) / N_STEPS
   __lowerCamelCase:					Optional[Any]	 =						function(snake_case			) + function(snake_case			)

   for i in range(1    ,   snake_case			):
      __lowerCamelCase:					Dict	 =						a + h * i
      result += function(snake_case			) * (4 if i % 2 else 2)

   result *= h / 3
   return round(snake_case    ,   snake_case			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()


