



from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

_lowercase: Any      			=		TypeVar("T")






def     a(      A       :    int       )		->       int:
					"""simple docstring"""





					return (position - 1) // 2






def     a(      A       :    int       )		->       int:
					"""simple docstring"""





					return (2 * position) + 1






def     a(      A       :    int       )		->       int:
					"""simple docstring"""





					return (2 * position) + 2



class 	_lowercase							(   Generic[T]	):





	"""simple docstring"""




	def __init__(self		):
						"""simple docstring"""

						a					     =   []
						a					     =   {}
						a					     =   0




	def __len__(self		):
						"""simple docstring"""

						return self.elements




	def __repr__(self		):
						"""simple docstring"""

						return str(self.heap		)




	def      UpperCamelCase_       (self		):
						"""simple docstring"""

						return self.elements == 0




	def      UpperCamelCase_       (self		,       lowerCamelCase_		,       lowerCamelCase_		):
						"""simple docstring"""

						self.heap.append((elem, weight)		)
						a					     =   self.elements
						self.elements += 1
						self._bubble_up(lowerCamelCase_		)




	def      UpperCamelCase_       (self		):
						"""simple docstring"""

						if self.elements > 1:
											self._swap_nodes(0		,       self.elements - 1		)
						a     ,				a					     =   self.heap.pop()
						del self.position_map[elem]
						self.elements -= 1
						if self.elements > 0:
											a     ,				a					     =   self.heap[0]
											self._bubble_down(lowerCamelCase_		)
						return elem




	def      UpperCamelCase_       (self		,       lowerCamelCase_		,       lowerCamelCase_		):
						"""simple docstring"""

						a					     =   self.position_map[elem]
						a					     =   (elem, weight)
						if position > 0:
											a					     =   get_parent_position(lowerCamelCase_		)
											a     ,				a					     =   self.heap[parent_position]
											if parent_weight > weight:
																self._bubble_up(lowerCamelCase_		)
											else:
																self._bubble_down(lowerCamelCase_		)
						else:
											self._bubble_down(lowerCamelCase_		)




	def      UpperCamelCase_       (self		,       lowerCamelCase_		):
						"""simple docstring"""

						a					     =   self.position_map[elem]
						if curr_pos == 0:
											return None
						a					     =   get_parent_position(lowerCamelCase_		)
						a     ,				a					     =   self.heap[curr_pos]
						a     ,				a					     =   self.heap[parent_position]
						if parent_weight > weight:
											self._swap_nodes(lowerCamelCase_		,       lowerCamelCase_		)
											return self._bubble_up(lowerCamelCase_		)
						return None




	def      UpperCamelCase_       (self		,       lowerCamelCase_		):
						"""simple docstring"""

						a					     =   self.position_map[elem]
						a     ,				a					     =   self.heap[curr_pos]
						a					     =   get_child_left_position(lowerCamelCase_		)
						a					     =   get_child_right_position(lowerCamelCase_		)
						if child_left_position < self.elements and child_right_position < self.elements:
											a     ,				a					     =   self.heap[child_left_position]
											a     ,				a					     =   self.heap[child_right_position]
											if child_right_weight < child_left_weight and child_right_weight < weight:
																self._swap_nodes(lowerCamelCase_		,       lowerCamelCase_		)
																return self._bubble_down(lowerCamelCase_		)
						if child_left_position < self.elements:
											a     ,				a					     =   self.heap[child_left_position]
											if child_left_weight < weight:
																self._swap_nodes(lowerCamelCase_		,       lowerCamelCase_		)
																return self._bubble_down(lowerCamelCase_		)
						else:
											return None
						if child_right_position < self.elements:
											a     ,				a					     =   self.heap[child_right_position]
											if child_right_weight < weight:
																self._swap_nodes(lowerCamelCase_		,       lowerCamelCase_		)
																return self._bubble_down(lowerCamelCase_		)
						return None




	def      UpperCamelCase_       (self		,       lowerCamelCase_		,       lowerCamelCase_		):
						"""simple docstring"""

						a					     =   self.heap[nodea_pos][0]
						a					     =   self.heap[nodea_pos][0]
						a     ,				a					     =   (
						    self.heap[nodea_pos],
						    self.heap[nodea_pos],
						)
						a					     =   nodea_pos
						a					     =   nodea_pos




class 	_lowercase							(   Generic[T]	):





	"""simple docstring"""




	def __init__(self		):
						"""simple docstring"""

						a					     =   {}
						a					     =   0




	def __repr__(self		):
						"""simple docstring"""

						return str(self.connections		)




	def __len__(self		):
						"""simple docstring"""

						return self.nodes




	def      UpperCamelCase_       (self		,       lowerCamelCase_		):
						"""simple docstring"""

						if node not in self.connections:
											a					     =   {}
											self.nodes += 1




	def      UpperCamelCase_       (self		,       lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_		):
						"""simple docstring"""

						self.add_node(lowerCamelCase_		)
						self.add_node(lowerCamelCase_		)
						a					     =   weight
						a					     =   weight






def     a(      A       :    GraphUndirectedWeighted[T] ,     )		->       tuple[dict[T, int], dict[T, T | None]]:
					"""simple docstring"""





					a					     =   {node: maxsize for node in graph.connections}
					a					     =   {node: None for node in graph.connections}

					a					     =   MinPriorityQueue()
					for node, weight in dist.items():
										priority_queue.push(A ,     A       )

					if priority_queue.is_empty():
										return dist, parent

					# initialization
					a					     =   priority_queue.extract_min()
					a					     =   0
					for neighbour in graph.connections[node]:
										if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
															a					     =   dist[node] + graph.connections[node][neighbour]
															priority_queue.update_key(A ,     dist[neighbour]       )
															a					     =   node

    # running prim's algorithm
					while not priority_queue.is_empty():
										a					     =   priority_queue.extract_min()
										for neighbour in graph.connections[node]:
															if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																				a					     =   dist[node] + graph.connections[node][neighbour]
																				priority_queue.update_key(A ,     dist[neighbour]       )
																				a					     =   node
					return dist, parent





# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput



class 	_lowercase							(   lowerCAmelCase	):





	"""simple docstring"""




	def __init__(self		,       lowerCamelCase_		,       lowerCamelCase_		):
						"""simple docstring"""

						super().__init__()
						self.register_modules(unet=lowerCamelCase_		,       scheduler=lowerCamelCase_		)




	@torch.no_grad()
	def __call__(self		,       lowerCamelCase_ = 1		,       lowerCamelCase_ = None		,       lowerCamelCase_ = 50		,       lowerCamelCase_ = "pil"		,       lowerCamelCase_ = True		,       **lowerCamelCase_		,       ):
						"""simple docstring"""

						a					     =   torch.randn(
						    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)		,       generator=lowerCamelCase_		,       )
						a					     =   image.to(self.device		)

						# set step values
						self.scheduler.set_timesteps(lowerCamelCase_		)

						for t in self.progress_bar(self.scheduler.timesteps		):
											# 1. predict noise model_output
											a					     =   self.unet(lowerCamelCase_		,       lowerCamelCase_		).sample

											# 2. predict previous mean of image x_t-1 and add variance depending on eta
											# eta corresponds to η in paper and should be between [0, 1]
											# do x_t -> x_t-1
											a					     =   self.scheduler.step(lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_		).prev_sample

						a					     =   (image / 2 + 0.5).clamp(0		,       1		)
						a					     =   image.cpu().permute(0		,       2		,       3		,       1		).numpy()
						if output_type == "pil":
											a					     =   self.numpy_to_pil(lowerCamelCase_		)

						if not return_dict:
											return (image,), "This is a local test"

						return ImagePipelineOutput(images=lowerCamelCase_		), "This is a local test"
