

class   __lowercase    :




			"""simple docstring"""







			def __init__(			self  :					List[Any]       ,						lowerCAmelCase__  :					Tuple       ,						lowerCAmelCase__  :					int):
									SCREAMING_SNAKE_CASE_:			Tuple  		=	name
									SCREAMING_SNAKE_CASE_:			List[str]  		=	val



			def __str__(			self  :					Any):
									return F"{self.__class__.__name__}({self.name}, {self.val})"




			def __lt__(			self  :					Any       ,						lowerCAmelCase__  :					Any):
									return self.val < other.val







class   __lowercase    :




			"""simple docstring"""







			def __init__(			self  :					str       ,						lowerCAmelCase__  :					Optional[Any]):
									SCREAMING_SNAKE_CASE_:			Optional[int]  		=	{}
									SCREAMING_SNAKE_CASE_:			Dict  		=	{}
									SCREAMING_SNAKE_CASE_:			Dict  		=	self.build_heap(lowerCAmelCase__)



			def __getitem__(			self  :					Dict       ,						lowerCAmelCase__  :					str):
									return self.get_value(lowerCAmelCase__)



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[Any]       ,						lowerCAmelCase__  :					Optional[Any]):
									return (idx - 1) // 2



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Dict       ,						lowerCAmelCase__  :					Union[str, Any]):
									return idx * 2 + 1



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[int]       ,						lowerCAmelCase__  :					str):
									return idx * 2 + 2



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[int]       ,						lowerCAmelCase__  :					List[str]):
									return self.heap_dict[key]



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Union[str, Any]       ,						lowerCAmelCase__  :					List[str]):
									SCREAMING_SNAKE_CASE_:			List[Any]  		=	len(lowerCAmelCase__) - 1
									SCREAMING_SNAKE_CASE_:			Any  		=	self.get_parent_idx(lowerCAmelCase__)

									for idx, i in enumerate(lowerCAmelCase__):
															SCREAMING_SNAKE_CASE_:			Dict  		=	idx
															SCREAMING_SNAKE_CASE_:			Optional[Any]  		=	i.val

									for i in range(lowerCAmelCase__       ,						-1       ,						-1):
															self.sift_down(lowerCAmelCase__       ,						lowerCAmelCase__)
									return array



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Union[str, Any]       ,						lowerCAmelCase__  :					Optional[Any]       ,						lowerCAmelCase__  :					List[Any]):
									while True:
															SCREAMING_SNAKE_CASE_:			int  		=	self.get_left_child_idx(lowerCAmelCase__)  # noqa: E741
															SCREAMING_SNAKE_CASE_:			int  		=	self.get_right_child_idx(lowerCAmelCase__)

															SCREAMING_SNAKE_CASE_:			Tuple  		=	idx
															if l < len(lowerCAmelCase__) and array[l] < array[idx]:
																					SCREAMING_SNAKE_CASE_:			str  		=	l
															if r < len(lowerCAmelCase__) and array[r] < array[smallest]:
																					SCREAMING_SNAKE_CASE_:			Any  		=	r

															if smallest != idx:
																					SCREAMING_SNAKE_CASE_		,   SCREAMING_SNAKE_CASE_:			Dict  		=	array[smallest], array[idx]
																					(
																					    (
																					    SCREAMING_SNAKE_CASE_
																					)		,   (
																					    SCREAMING_SNAKE_CASE_
																					)		,   
																					):			List[str]  		=	(
																					    self.idx_of_element[array[smallest]],
																					    self.idx_of_element[array[idx]],
																					)
																					SCREAMING_SNAKE_CASE_:			List[str]  		=	smallest
															else:
																					break



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[int]       ,						lowerCAmelCase__  :					str):
									SCREAMING_SNAKE_CASE_:			Union[str, Any]  		=	self.get_parent_idx(lowerCAmelCase__)
									while p >= 0 and self.heap[p] > self.heap[idx]:
															SCREAMING_SNAKE_CASE_		,   SCREAMING_SNAKE_CASE_:			str  		=	self.heap[idx], self.heap[p]
															SCREAMING_SNAKE_CASE_		,   SCREAMING_SNAKE_CASE_:			Tuple  		=	(
															    self.idx_of_element[self.heap[idx]],
															    self.idx_of_element[self.heap[p]],
															)
															SCREAMING_SNAKE_CASE_:			Dict  		=	p
															SCREAMING_SNAKE_CASE_:			Any  		=	self.get_parent_idx(lowerCAmelCase__)



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Optional[int]):
									return self.heap[0]



			def 	_SCREAMING_SNAKE_CASE      (			self  :					Tuple):
									SCREAMING_SNAKE_CASE_		,   SCREAMING_SNAKE_CASE_:			List[Any]  		=	self.heap[-1], self.heap[0]
									SCREAMING_SNAKE_CASE_		,   SCREAMING_SNAKE_CASE_:			List[Any]  		=	(
									    self.idx_of_element[self.heap[-1]],
									    self.idx_of_element[self.heap[0]],
									)

									SCREAMING_SNAKE_CASE_:			str  		=	self.heap.pop()
									del self.idx_of_element[x]
									self.sift_down(0       ,						self.heap)
									return x



			def 	_SCREAMING_SNAKE_CASE      (			self  :					List[str]       ,						lowerCAmelCase__  :					Union[str, Any]):
									self.heap.append(lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_:			List[str]  		=	len(self.heap) - 1
									SCREAMING_SNAKE_CASE_:			Any  		=	node.val
									self.sift_up(len(self.heap) - 1)



			def 	_SCREAMING_SNAKE_CASE      (			self  :					str):
									return len(self.heap) == 0




			def 	_SCREAMING_SNAKE_CASE      (			self  :					Union[str, Any]       ,						lowerCAmelCase__  :					Any       ,						lowerCAmelCase__  :					Optional[Any]):
									assert (
									    self.heap[self.idx_of_element[node]].val > new_value
									), "newValue must be less that current value"
									SCREAMING_SNAKE_CASE_:			Union[str, Any]  		=	new_value
									SCREAMING_SNAKE_CASE_:			List[Any]  		=	new_value
									self.sift_up(self.idx_of_element[node])







lowerCAmelCase							:  List[Any]            =						Node("""R""", -1)
lowerCAmelCase							:  Union[str, Any]            =						Node("""B""", 6)
lowerCAmelCase							:  int            =						Node("""A""", 3)
lowerCAmelCase							:  Any            =						Node("""X""", 1)
lowerCAmelCase							:  Optional[Any]            =						Node("""E""", 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
lowerCAmelCase							:  Any            =						MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print("""Min Heap - before decrease key""")
for i in my_min_heap.heap:
						print(i)

print("""Min Heap - After decrease key of node [B -> -17]""")
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
						print(i)

if __name__ == "__main__":
						import doctest

						doctest.testmod()









def       A_				(   _UpperCAmelCase    ,     _UpperCAmelCase   ):

						if density <= 0:
												raise ValueError("Impossible fluid density"   )
						if bulk_modulus <= 0:
												raise ValueError("Impossible bulk modulus"   )

						return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
						import doctest

						doctest.testmod()






