




class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					List[str]:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						name
				SCREAMING_SNAKE_CASE_								=						val





	def __str__(							self      )  ->					Any:




				"""simple docstring"""



				return f'{self.__class__.__name__}({self.name}, {self.val})'





	def __lt__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					List[str]:




				"""simple docstring"""



				return self.val < other.val




class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Optional[Any]:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						{}
				SCREAMING_SNAKE_CASE_								=						{}
				SCREAMING_SNAKE_CASE_								=						self.build_heap(SCREAMING_SNAKE_CASE      )





	def __getitem__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Tuple:




				"""simple docstring"""



				return self.get_value(SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					int:




				"""simple docstring"""



				return (idx - 1) // 2





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					int:




				"""simple docstring"""



				return idx * 2 + 1





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Any:




				"""simple docstring"""



				return idx * 2 + 2





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Optional[int]:




				"""simple docstring"""



				return self.heap_dict[key]





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Any:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						len(SCREAMING_SNAKE_CASE      ) - 1
				SCREAMING_SNAKE_CASE_								=						self.get_parent_idx(SCREAMING_SNAKE_CASE      )

				for idx, i in enumerate(SCREAMING_SNAKE_CASE      ):
							SCREAMING_SNAKE_CASE_								=						idx
							SCREAMING_SNAKE_CASE_								=						i.val

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





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					Any:




				"""simple docstring"""



				while True:
							SCREAMING_SNAKE_CASE_								=						self.get_left_child_idx(SCREAMING_SNAKE_CASE      )  # noqa: E741
							SCREAMING_SNAKE_CASE_								=						self.get_right_child_idx(SCREAMING_SNAKE_CASE      )

							SCREAMING_SNAKE_CASE_								=						idx
							if l < len(SCREAMING_SNAKE_CASE      ) and array[l] < array[idx]:
										SCREAMING_SNAKE_CASE_								=						l
							if r < len(SCREAMING_SNAKE_CASE      ) and array[r] < array[smallest]:
										SCREAMING_SNAKE_CASE_								=						r

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





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Dict:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						self.get_parent_idx(SCREAMING_SNAKE_CASE      )
				while p >= 0 and self.heap[p] > self.heap[idx]:
							SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						self.heap[idx], self.heap[p]
							SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						(
							    self.idx_of_element[self.heap[idx]],
							    self.idx_of_element[self.heap[p]],
							)
							SCREAMING_SNAKE_CASE_								=						p
							SCREAMING_SNAKE_CASE_								=						self.get_parent_idx(SCREAMING_SNAKE_CASE      )





	def 						A_(							self      )  ->					Optional[Any]:




				"""simple docstring"""



				return self.heap[0]





	def 						A_(							self      )  ->					Optional[int]:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						self.heap[-1], self.heap[0]
				SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						(
				    self.idx_of_element[self.heap[-1]],
				    self.idx_of_element[self.heap[0]],
				)

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





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Dict:




				"""simple docstring"""



				self.heap.append(SCREAMING_SNAKE_CASE      )
				SCREAMING_SNAKE_CASE_								=						len(self.heap      ) - 1
				SCREAMING_SNAKE_CASE_								=						node.val
				self.sift_up(len(self.heap      ) - 1      )





	def 						A_(							self      )  ->					int:




				"""simple docstring"""



				return len(self.heap      ) == 0





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					Optional[int]:




				"""simple docstring"""



				assert (
				    self.heap[self.idx_of_element[node]].val > new_value
				), "newValue must be less that current value"
				SCREAMING_SNAKE_CASE_								=						new_value
				SCREAMING_SNAKE_CASE_								=						new_value
				self.sift_up(self.idx_of_element[node]      )




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

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

# Generating Min-Heap from array
SCREAMING_SNAKE_CASE__     :     int		    =       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()






import qiskit

def lowercase    (  SCREAMING_SNAKE_CASE = 2 )			->							qiskit.result.counts.Counts:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						qubits

			# Using Aer's simulator
			SCREAMING_SNAKE_CASE_								=						qiskit.Aer.get_backend('aer_simulator' )

			# Creating a Quantum Circuit acting on the q register
			SCREAMING_SNAKE_CASE_								=						qiskit.QuantumCircuit(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )

			# Adding a H gate on qubit 0 (now q0 in superposition)
			circuit.h(0 )

			for i in range(1       ,    SCREAMING_SNAKE_CASE ):
						# Adding CX (CNOT) gate
						circuit.cx(i - 1       ,    SCREAMING_SNAKE_CASE )

			# Mapping the quantum measurement to the classical bits
			circuit.measure(list(range(SCREAMING_SNAKE_CASE ) )       ,    list(range(SCREAMING_SNAKE_CASE ) ) )

			# Now measuring any one qubit would affect other qubits to collapse
			# their super position and have same state as the measured one.

			# Executing the circuit on the simulator
			SCREAMING_SNAKE_CASE_								=						qiskit.execute(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    shots=10_00 )

			return job.result().get_counts(SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
				print(f"""Total count for various states are: {quantum_entanglement(3)}""")
