






"""simple docstring"""






def  __lowerCamelCase					(					lowerCAmelCase__				):

				# bit count represents no. of bits in the gray code
				if bit_count < 0:
								raise ValueError('The given input must be positive'				)

				# get the generated string sequence
				A__							 =       gray_code_sequence_string(a_				)
				#
				# convert them to integers
				for i in range(len(a_				)				):
								A__							 =       int(sequence[i]       ,2				)

				return sequence



def  __lowerCamelCase					(					lowerCAmelCase__				):

				# The approach is a recursive one
				# Base case achieved when either n = 0 or n=1
				if bit_count == 0:
								return ["0"]

				if bit_count == 1:
								return ["0", "1"]

				A__							 =       1 << bit_count  # defines the length of the sequence
				# 1<< n is equivalent to 2^n

				# recursive answer will generate answer for n-1 bits
				A__							 =       gray_code_sequence_string(bit_count - 1				)

				A__							 =       []

				# append 0 to first half of the smaller sequence generated
				for i in range(seq_len // 2				):
								A__							 =       '''0''' + smaller_sequence[i]
								sequence.append(a_				)

				# append 1 to second half ... start from the end of the list
				for i in reversed(range(seq_len // 2				)				):
								A__							 =       '''1''' + smaller_sequence[i]
								sequence.append(a_				)

				return sequence


if __name__ == "__main__":
					import doctest

					doctest.testmod()










"""simple docstring"""






class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					A__							 =       name
					A__							 =       val


	def __str__(      self						):


					"""simple docstring"""

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






	def __lt__(      self  ,					__a						):


					"""simple docstring"""

					return self.val < other.val





class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       {}
					A__							 =       {}
					A__							 =       self.build_heap(__a						)


	def __getitem__(      self  ,					__a						):


					"""simple docstring"""

					return self.get_value(__a						)


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return (idx - 1) // 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 1


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return self.heap_dict[key]


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       len(__a						) - 1
					A__							 =       self.get_parent_idx(__a						)

					for idx, i in enumerate(__a						):
									A__							 =       idx
									A__							 =       i.val

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


	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					while True:
									A__							 =       self.get_left_child_idx(__a						)  # noqa: E741
									A__							 =       self.get_right_child_idx(__a						)

									A__							 =       idx
									if l < len(__a						) and array[l] < array[idx]:
													A__							 =       l
									if r < len(__a						) and array[r] < array[smallest]:
													A__							 =       r

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


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

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


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return self.heap[0]


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

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

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


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					self.heap.append(__a						)
					A__							 =       len(self.heap						) - 1
					A__							 =       node.val
					self.sift_up(len(self.heap						) - 1						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return len(self.heap						) == 0






	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

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





SCREAMING_SNAKE_CASE						:						List[str]					   =       Node('''R''', -1)
SCREAMING_SNAKE_CASE						:						Tuple					   =       Node('''B''', 6)
SCREAMING_SNAKE_CASE						:						List[Any]					   =       Node('''A''', 3)
SCREAMING_SNAKE_CASE						:						int					   =       Node('''X''', 1)
SCREAMING_SNAKE_CASE						:						Union[str, Any]					   =       Node('''E''', 4)

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

# Generating Min-Heap from array
SCREAMING_SNAKE_CASE						:						str					   =       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()


