


'''simple docstring'''

import gc
import unittest

import numpy as np
import torch
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    PNDMScheduler,
    StableDiffusionLDMaDPipeline,
    UNetaDConditionModel,
)
from diffusers.utils import nightly, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu

from ..pipeline_params import TEXT_TO_IMAGE_BATCH_PARAMS, TEXT_TO_IMAGE_IMAGE_PARAMS, TEXT_TO_IMAGE_PARAMS


enable_full_determinism()
class _lowerCamelCase	(						unittest.TestCase							):



		'''simple docstring'''







		A_     :      Union[str, Any]				   =    StableDiffusionLDMaDPipeline
		A_     :      List[Any]				   =    TEXT_TO_IMAGE_PARAMS
		A_     :      Any				   =    TEXT_TO_IMAGE_BATCH_PARAMS
		A_     :      int				   =    TEXT_TO_IMAGE_IMAGE_PARAMS







		def        __lowerCAmelCase		( self		:						List[str]      )  ->			str:
			torch.manual_seed(0      )
			__magic_name__	:   List[str]					     =					UNetaDConditionModel(
			    block_out_channels=(32, 64)  ,					layers_per_block=2  ,					sample_size=32  ,					in_channels=4  ,					out_channels=4  ,					down_block_types=('DownBlock2D', 'CrossAttnDownBlock2D')  ,					up_block_types=('CrossAttnUpBlock2D', 'UpBlock2D')  ,					cross_attention_dim=32  ,					)
			__magic_name__	:   str					     =					DDIMScheduler(
			    beta_start=0.0_0085  ,					beta_end=0.012  ,					beta_schedule='scaled_linear'  ,					clip_sample=_SCREAMING_SNAKE_CASE  ,					set_alpha_to_one=_SCREAMING_SNAKE_CASE  ,					)
			torch.manual_seed(0      )
			__magic_name__	:   List[Any]					     =					AutoencoderKL(
			    block_out_channels=[32, 64]  ,					in_channels=6  ,					out_channels=6  ,					down_block_types=['DownEncoderBlock2D', 'DownEncoderBlock2D']  ,					up_block_types=['UpDecoderBlock2D', 'UpDecoderBlock2D']  ,					latent_channels=4  ,					)
			torch.manual_seed(0      )
			__magic_name__	:   Tuple					     =					CLIPTextConfig(
			    bos_token_id=0  ,					eos_token_id=2  ,					hidden_size=32  ,					intermediate_size=37  ,					layer_norm_eps=1E-05  ,					num_attention_heads=4  ,					num_hidden_layers=5  ,					pad_token_id=1  ,					vocab_size=1000  ,					)
			__magic_name__	:   str					     =					CLIPTextModel(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Dict					     =					CLIPTokenizer.from_pretrained('hf-internal-testing/tiny-random-clip'      )

			__magic_name__	:   Optional[int]					     =					{
			    '''unet''': unet,
			    '''scheduler''': scheduler,
			    '''vae''': vae,
			    '''text_encoder''': text_encoder,
			    '''tokenizer''': tokenizer,
			    '''safety_checker''': None,
			    '''feature_extractor''': None,
			}
			return components







		def        __lowerCAmelCase		( self		:						Union[str, Any]  ,					_A		:						int  ,					_A		:						Optional[int]=0      )  ->			Dict:





			if str(_SCREAMING_SNAKE_CASE      ).startswith('mps'      ):
				__magic_name__	:   Tuple					     =					torch.manual_seed(_SCREAMING_SNAKE_CASE      )
			else:
				__magic_name__	:   List[Any]					     =					torch.Generator(device=_SCREAMING_SNAKE_CASE      ).manual_seed(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   List[Any]					     =					{
			    '''prompt''': '''A painting of a squirrel eating a burger''',
			    '''generator''': generator,
			    '''num_inference_steps''': 2,
			    '''guidance_scale''': 6.0,
			    '''output_type''': '''numpy''',
			}
			return inputs







		def        __lowerCAmelCase		( self		:						Union[str, Any]      )  ->			int:
			__magic_name__	:   int					     =					'''cpu'''  # ensure determinism for the device-dependent torch.Generator

			__magic_name__	:   List[Any]					     =					self.get_dummy_components()
			__magic_name__	:   Union[str, Any]					     =					StableDiffusionLDMaDPipeline(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Dict					     =					ldmad_pipe.to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   Optional[int]					     =					self.get_dummy_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Tuple					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Optional[Any]					     =					output.rgb, output.depth

			__magic_name__	:   List[Any]					     =					rgb[0, -3:, -3:, -1]
			__magic_name__	:   Union[str, Any]					     =					depth[0, -3:, -1]

			assert rgb.shape == (1, 64, 64, 3)
			assert depth.shape == (1, 64, 64)

			__magic_name__	:   Tuple					     =					np.array(
			    [0.3733_8176, 0.7_0247, 0.7420_3193, 0.5164_3604, 0.5825_6793, 0.6093_2136, 0.418_1095, 0.4835_5877, 0.4653_5262]      )
			__magic_name__	:   Union[str, Any]					     =					np.array([103.46727, 85.812004, 87.849236]      )

			assert np.abs(image_slice_rgb.flatten() - expected_slice_rgb      ).max() < 1E-2
			assert np.abs(image_slice_depth.flatten() - expected_slice_depth      ).max() < 1E-2







		def        __lowerCAmelCase		( self		:						Dict      )  ->			int:
			__magic_name__	:   Optional[Any]					     =					self.get_dummy_components()
			__magic_name__	:   Any					     =					StableDiffusionLDMaDPipeline(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   List[str]					     =					ldmad_pipe.to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   List[Any]					     =					self.get_dummy_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   str					     =					3 * [inputs['''prompt''']]

			# forward
			__magic_name__	:   Optional[Any]					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Optional[int]					     =					output.rgb, output.depth
			__magic_name__	:   Tuple					     =					rgb_slice_a[0, -3:, -3:, -1]
			__magic_name__	:   Optional[Any]					     =					depth_slice_a[0, -3:, -1]

			__magic_name__	:   Tuple					     =					self.get_dummy_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Dict					     =					3 * [inputs.pop('prompt'      )]

			__magic_name__	:   Tuple					     =					ldmad_pipe.tokenizer(
			    _SCREAMING_SNAKE_CASE  ,					padding='max_length'  ,					max_length=ldmad_pipe.tokenizer.model_max_length  ,					truncation=_SCREAMING_SNAKE_CASE  ,					return_tensors='pt'  ,					)
			__magic_name__	:   Dict					     =					text_inputs['''input_ids'''].to(_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   Optional[Any]					     =					ldmad_pipe.text_encoder(_SCREAMING_SNAKE_CASE      )[0]

			__magic_name__	:   Optional[int]					     =					prompt_embeds

			# forward
			__magic_name__	:   Optional[int]					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Any					     =					output.rgb, output.depth
			__magic_name__	:   Any					     =					rgb_slice_a[0, -3:, -3:, -1]
			__magic_name__	:   str					     =					depth_slice_a[0, -3:, -1]

			assert np.abs(rgb_slice_a.flatten() - rgb_slice_a.flatten()      ).max() < 1E-4
			assert np.abs(depth_slice_a.flatten() - depth_slice_a.flatten()      ).max() < 1E-4







		def        __lowerCAmelCase		( self		:						Dict      )  ->			Union[str, Any]:
			__magic_name__	:   Tuple					     =					'''cpu'''  # ensure determinism for the device-dependent torch.Generator
			__magic_name__	:   List[str]					     =					self.get_dummy_components()
			__magic_name__	:   int					     =					PNDMScheduler(skip_prk_steps=_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   int					     =					StableDiffusionLDMaDPipeline(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   str					     =					ldmad_pipe.to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   str					     =					self.get_dummy_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   List[Any]					     =					'''french fries'''
			__magic_name__	:   Optional[Any]					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE  ,					negative_prompt=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   Optional[int]					     =					output.rgb, output.depth
			__magic_name__	:   Optional[Any]					     =					rgb[0, -3:, -3:, -1]
			__magic_name__	:   int					     =					depth[0, -3:, -1]

			assert rgb.shape == (1, 64, 64, 3)
			assert depth.shape == (1, 64, 64)

			__magic_name__	:   int					     =					np.array(
			    [0.3_7044, 0.7181_1503, 0.722_3251, 0.4860_3675, 0.563_8391, 0.636_4948, 0.4283_3704, 0.490_1315, 0.4792_6217]      )
			__magic_name__	:   Any					     =					np.array([107.84738, 84.62802, 89.962135]      )
			assert np.abs(rgb_slice.flatten() - expected_slice_rgb      ).max() < 1E-2
			assert np.abs(depth_slice.flatten() - expected_slice_depth      ).max() < 1E-2







@slow
@require_torch_gpu
class _lowerCamelCase	(						unittest.TestCase							):



		'''simple docstring'''







		def        __lowerCAmelCase		( self		:						Optional[Any]      )  ->			str:
			super().tearDown()
			gc.collect()
			torch.cuda.empty_cache()







		def        __lowerCAmelCase		( self		:						Union[str, Any]  ,					_A		:						Optional[int]  ,					_A		:						Tuple="cpu"  ,					_A		:						str=torch.floataa  ,					_A		:						Any=0      )  ->			Optional[int]:
			__magic_name__	:   Union[str, Any]					     =					torch.Generator(device=_SCREAMING_SNAKE_CASE      ).manual_seed(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   str					     =					np.random.RandomState(_SCREAMING_SNAKE_CASE      ).standard_normal((1, 4, 64, 64)      )
			__magic_name__	:   int					     =					torch.from_numpy(_SCREAMING_SNAKE_CASE      ).to(device=_SCREAMING_SNAKE_CASE  ,					dtype=_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   int					     =					{
			    '''prompt''': '''a photograph of an astronaut riding a horse''',
			    '''latents''': latents,
			    '''generator''': generator,
			    '''num_inference_steps''': 3,
			    '''guidance_scale''': 7.5,
			    '''output_type''': '''numpy''',
			}
			return inputs







		def        __lowerCAmelCase		( self		:						Optional[Any]      )  ->			str:
			__magic_name__	:   List[str]					     =					StableDiffusionLDMaDPipeline.from_pretrained('Intel/ldm3d'      )
			__magic_name__	:   Optional[Any]					     =					ldmad_pipe.to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   int					     =					self.get_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Dict					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Union[str, Any]					     =					output.rgb, output.depth
			__magic_name__	:   int					     =					rgb[0, -3:, -3:, -1].flatten()
			__magic_name__	:   Union[str, Any]					     =					rgb[0, -3:, -1].flatten()

			assert rgb.shape == (1, 512, 512, 3)
			assert depth.shape == (1, 512, 512)

			__magic_name__	:   Tuple					     =					np.array(
			    [0.5380_5465, 0.5670_7305, 0.548_6515, 0.5701_2236, 0.581_4511, 0.5625_3487, 0.5484_3014, 0.5509_2263, 0.645_9706]      )
			__magic_name__	:   Tuple					     =					np.array(
			    [0.926_3781, 0.667_8672, 0.548_6515, 0.9220_2145, 0.6783_1135, 0.5625_3487, 0.924_1694, 0.755_1478, 0.645_9706]      )
			assert np.abs(rgb_slice - expected_slice_rgb      ).max() < 3E-3
			assert np.abs(depth_slice - expected_slice_depth      ).max() < 3E-3







@nightly
@require_torch_gpu
class _lowerCamelCase	(						unittest.TestCase							):



		'''simple docstring'''







		def        __lowerCAmelCase		( self		:						List[Any]      )  ->			Tuple:
			super().tearDown()
			gc.collect()
			torch.cuda.empty_cache()







		def        __lowerCAmelCase		( self		:						Optional[int]  ,					_A		:						List[str]  ,					_A		:						Dict="cpu"  ,					_A		:						str=torch.floataa  ,					_A		:						str=0      )  ->			int:
			__magic_name__	:   Optional[Any]					     =					torch.Generator(device=_SCREAMING_SNAKE_CASE      ).manual_seed(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Any					     =					np.random.RandomState(_SCREAMING_SNAKE_CASE      ).standard_normal((1, 4, 64, 64)      )
			__magic_name__	:   str					     =					torch.from_numpy(_SCREAMING_SNAKE_CASE      ).to(device=_SCREAMING_SNAKE_CASE  ,					dtype=_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   List[Any]					     =					{
			    '''prompt''': '''a photograph of an astronaut riding a horse''',
			    '''latents''': latents,
			    '''generator''': generator,
			    '''num_inference_steps''': 50,
			    '''guidance_scale''': 7.5,
			    '''output_type''': '''numpy''',
			}
			return inputs







		def        __lowerCAmelCase		( self		:						Optional[Any]      )  ->			int:
			__magic_name__	:   Tuple					     =					StableDiffusionLDMaDPipeline.from_pretrained('Intel/ldm3d'      ).to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   List[Any]					     =					self.get_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   str					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   List[Any]					     =					output.rgb, output.depth

			__magic_name__	:   int					     =					0.49_5586
			__magic_name__	:   Union[str, Any]					     =					0.3379_5515
			__magic_name__	:   Optional[int]					     =					112.48518
			__magic_name__	:   Optional[Any]					     =					98.489746
			assert np.abs(expected_rgb_mean - rgb.mean()      ) < 1E-3
			assert np.abs(expected_rgb_std - rgb.std()      ) < 1E-3
			assert np.abs(expected_depth_mean - depth.mean()      ) < 1E-3
			assert np.abs(expected_depth_std - depth.std()      ) < 1E-3







		def        __lowerCAmelCase		( self		:						List[Any]      )  ->			Optional[Any]:
			__magic_name__	:   Any					     =					StableDiffusionLDMaDPipeline.from_pretrained('Intel/ldm3d-4c'      ).to(_SCREAMING_SNAKE_CASE      )
			ldmad_pipe.set_progress_bar_config(disable=_SCREAMING_SNAKE_CASE      )

			__magic_name__	:   Optional[Any]					     =					self.get_inputs(_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Tuple					     =					ldmad_pipe(**_SCREAMING_SNAKE_CASE      )
			__magic_name__	:   Optional[Any]					     =					output.rgb, output.depth

			__magic_name__	:   Tuple					     =					0.419_4127
			__magic_name__	:   Union[str, Any]					     =					0.3537_5586
			__magic_name__	:   Union[str, Any]					     =					0.563_8502
			__magic_name__	:   List[Any]					     =					0.3468_6103

			assert rgb.shape == (1, 512, 512, 3)
			assert depth.shape == (1, 512, 512, 1)
			assert np.abs(expected_rgb_mean - rgb.mean()      ) < 1E-3
			assert np.abs(expected_rgb_std - rgb.std()      ) < 1E-3
			assert np.abs(expected_depth_mean - depth.mean()      ) < 1E-3
			assert np.abs(expected_depth_std - depth.std()      ) < 1E-3



'''simple docstring'''

from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

lowerCAmelCase				:Any        =      TypeVar('''T''')





def lowerCamelCase      (      lowerCAmelCase    :     int		):





	"""simple docstring"""







	return (position - 1) // 2





def lowerCamelCase      (      lowerCAmelCase    :     int		):





	"""simple docstring"""







	return (2 * position) + 1





def lowerCamelCase      (      lowerCAmelCase    :     int		):





	"""simple docstring"""







	return (2 * position) + 2
class _lowerCamelCase	(						Generic[T]							):



		'''simple docstring'''







		def __init__( self		:						Union[str, Any]      )  ->			None:
			__magic_name__	:   list[tuple[T, int]]					     =					[]
			__magic_name__	:   dict[T, int]					     =					{}
			__magic_name__	:   int					     =					0







		def __len__( self		:						Optional[int]      )  ->			int:
			return self.elements







		def __repr__( self		:						Optional[Any]      )  ->			str:
			return str(self.heap      )







		def        __lowerCAmelCase		( self		:						List[Any]      )  ->			bool:
			# Check if the priority queue is empty
			return self.elements == 0







		def        __lowerCAmelCase		( self		:						Dict  ,					_A		:						T  ,					_A		:						int      )  ->			None:
			# Add an element with given priority to the queue
			self.heap.append((elem, weight)      )
			__magic_name__	:   List[str]					     =					self.elements
			self.elements += 1
			self._bubble_up(_A      )







		def        __lowerCAmelCase		( self		:						List[Any]      )  ->			T:
			# Remove and return the element with lowest weight (highest priority)
			if self.elements > 1:
				self._swap_nodes(0  ,					self.elements - 1      )
			__magic_name__     ,    __magic_name__	:   Optional[Any]					     =					self.heap.pop()
			del self.position_map[elem]
			self.elements -= 1
			if self.elements > 0:
				__magic_name__     ,    __magic_name__	:   Tuple					     =					self.heap[0]
				self._bubble_down(_A      )
			return elem







		def        __lowerCAmelCase		( self		:						Dict  ,					_A		:						T  ,					_A		:						int      )  ->			None:
			# Update the weight of the given key
			__magic_name__	:   Optional[Any]					     =					self.position_map[elem]
			__magic_name__	:   Any					     =					(elem, weight)
			if position > 0:
				__magic_name__	:   Optional[int]					     =					get_parent_position(_A      )
				__magic_name__     ,    __magic_name__	:   Any					     =					self.heap[parent_position]
				if parent_weight > weight:
					self._bubble_up(_A      )
				else:
					self._bubble_down(_A      )
			else:
				self._bubble_down(_A      )







		def        __lowerCAmelCase		( self		:						Optional[int]  ,					_A		:						T      )  ->			None:
			# Place a node at the proper position (upward movement) [to be used internally
			# only]
			__magic_name__	:   Union[str, Any]					     =					self.position_map[elem]
			if curr_pos == 0:
				return None
			__magic_name__	:   Optional[Any]					     =					get_parent_position(_A      )
			__magic_name__     ,    __magic_name__	:   Any					     =					self.heap[curr_pos]
			__magic_name__     ,    __magic_name__	:   int					     =					self.heap[parent_position]
			if parent_weight > weight:
				self._swap_nodes(_A  ,					_A      )
				return self._bubble_up(_A      )
			return None







		def        __lowerCAmelCase		( self		:						int  ,					_A		:						T      )  ->			None:
			# Place a node at the proper position (downward movement) [to be used
			# internally only]
			__magic_name__	:   Dict					     =					self.position_map[elem]
			__magic_name__     ,    __magic_name__	:   List[str]					     =					self.heap[curr_pos]
			__magic_name__	:   str					     =					get_child_left_position(_A      )
			__magic_name__	:   List[str]					     =					get_child_right_position(_A      )
			if child_left_position < self.elements and child_right_position < self.elements:
				__magic_name__     ,    __magic_name__	:   int					     =					self.heap[child_left_position]
				__magic_name__     ,    __magic_name__	:   int					     =					self.heap[child_right_position]
				if child_right_weight < child_left_weight and child_right_weight < weight:
					self._swap_nodes(_A  ,					_A      )
					return self._bubble_down(_A      )
			if child_left_position < self.elements:
				__magic_name__     ,    __magic_name__	:   Any					     =					self.heap[child_left_position]
				if child_left_weight < weight:
					self._swap_nodes(_A  ,					_A      )
					return self._bubble_down(_A      )
			else:
				return None
			if child_right_position < self.elements:
				__magic_name__     ,    __magic_name__	:   str					     =					self.heap[child_right_position]
				if child_right_weight < weight:
					self._swap_nodes(_A  ,					_A      )
					return self._bubble_down(_A      )
			return None







		def        __lowerCAmelCase		( self		:						int  ,					_A		:						int  ,					_A		:						int      )  ->			None:
			# Swap the nodes at the given positions
			__magic_name__	:   List[Any]					     =					self.heap[nodea_pos][0]
			__magic_name__	:   Union[str, Any]					     =					self.heap[nodea_pos][0]
			__magic_name__     ,    __magic_name__	:   Optional[Any]					     =					(
			    self.heap[nodea_pos],
			    self.heap[nodea_pos],
			)
			__magic_name__	:   Optional[Any]					     =					nodea_pos
			__magic_name__	:   Optional[Any]					     =					nodea_pos







class _lowerCamelCase	(						Generic[T]							):



		'''simple docstring'''







		def __init__( self		:						Union[str, Any]      )  ->			None:
			__magic_name__	:   dict[T, dict[T, int]]					     =					{}
			__magic_name__	:   int					     =					0







		def __repr__( self		:						str      )  ->			str:
			return str(self.connections      )







		def __len__( self		:						Union[str, Any]      )  ->			int:
			return self.nodes







		def        __lowerCAmelCase		( self		:						Dict  ,					_A		:						T      )  ->			None:
			# Add a node in the graph if it is not in the graph
			if node not in self.connections:
				__magic_name__	:   str					     =					{}
				self.nodes += 1







		def        __lowerCAmelCase		( self		:						List[str]  ,					_A		:						T  ,					_A		:						T  ,					_A		:						int      )  ->			None:
			# Add an edge between 2 nodes in the graph
			self.add_node(_A      )
			self.add_node(_A      )
			__magic_name__	:   Any					     =					weight
			__magic_name__	:   Dict					     =					weight







def lowerCamelCase      (      lowerCAmelCase    :     GraphUndirectedWeighted[T]		,		):





	"""simple docstring"""







	__magic_name__	:   dict[T, int]					     =					{node: maxsize for node in graph.connections}
	__magic_name__	:   dict[T, T | None]					     =					{node: None for node in graph.connections}

	__magic_name__	:   MinPriorityQueue[T]					     =					MinPriorityQueue()
	for node, weight in dist.items():
		priority_queue.push(lowerCAmelCase		,		lowerCAmelCase		)

	if priority_queue.is_empty():
		return dist, parent

	# initialization
	__magic_name__	:   Any					     =					priority_queue.extract_min()
	__magic_name__	:   List[str]					     =					0
	for neighbour in graph.connections[node]:
		if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
			__magic_name__	:   Any					     =					dist[node] + graph.connections[node][neighbour]
			priority_queue.update_key(lowerCAmelCase		,		dist[neighbour]		)
			__magic_name__	:   Tuple					     =					node

    # running prim's algorithm
	while not priority_queue.is_empty():
		__magic_name__	:   Tuple					     =					priority_queue.extract_min()
		for neighbour in graph.connections[node]:
			if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
				__magic_name__	:   int					     =					dist[node] + graph.connections[node][neighbour]
				priority_queue.update_key(lowerCAmelCase		,		dist[neighbour]		)
				__magic_name__	:   Union[str, Any]					     =					node
	return dist, parent