





'''simple docstring'''







from __future__ import annotations

from queue import Queue





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     int,     SCREAMING_SNAKE_CASE__ :     int				)	->		tuple[int, int]:
						a ^= b
						b ^= a
						a ^= b
						return a, b





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     int,     SCREAMING_SNAKE_CASE__ :     list[list[int]]				)	->		list[list[int]]:
						UpperCAmelCase_     : Union[str, Any]         =					1
						while (1 << j) < max_node:
												for i in range(1,     max_node + 1				):
																		UpperCAmelCase_     : List[Any]         =					parent[j - 1][parent[j - 1][i]]
												j += 1
						return parent





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     int,     SCREAMING_SNAKE_CASE__ :     int,     SCREAMING_SNAKE_CASE__ :     list[int],     SCREAMING_SNAKE_CASE__ :     list[list[int]]				)	->		int:
						# u must be deeper in the tree than v
						if level[u] < level[v]:
												UpperCAmelCase_  ,    UpperCAmelCase_     : int         =					swap(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)
						# making depth of u same as depth of v
						for i in range(18,     -1,     -1				):
												if level[u] - (1 << i) >= level[v]:
																		UpperCAmelCase_     : Tuple         =					parent[i][u]
    # at the same depth if u==v that mean lca is found
						if u == v:
												return u
						# moving both nodes upwards till lca in found
						for i in range(18,     -1,     -1				):
												if parent[i][u] not in [0, parent[i][v]]:
																		UpperCAmelCase_  ,    UpperCAmelCase_     : List[Any]         =					parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
						return parent[0][u]





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     list[int],     SCREAMING_SNAKE_CASE__ :     list[list[int]],     SCREAMING_SNAKE_CASE__ :     int,     SCREAMING_SNAKE_CASE__ :     dict[int, list[int]],     SCREAMING_SNAKE_CASE__ :     int = 1,     )	->		tuple[list[int], list[list[int]]]:
						UpperCAmelCase_     : str         =					0
						UpperCAmelCase_     : Queue[int]         =					Queue(maxsize=SCREAMING_SNAKE_CASE__				)
						q.put(SCREAMING_SNAKE_CASE__				)
						while q.qsize() != 0:
												UpperCAmelCase_     : Tuple         =					q.get()
												for v in graph[u]:
																		if level[v] == -1:
																								UpperCAmelCase_     : Dict         =					level[u] + 1
																								q.put(SCREAMING_SNAKE_CASE__				)
																								UpperCAmelCase_     : Optional[Any]         =					u
						return level, parent





def     lowerCamelCase_ (					)	->		None:
						UpperCAmelCase_     : Optional[int]         =					13
						# initializing with 0
						UpperCAmelCase_     : Any         =					[[0 for _ in range(max_node + 10				)] for _ in range(20				)]
						# initializing with -1 which means every node is unvisited
						UpperCAmelCase_     : str         =					[-1 for _ in range(max_node + 10				)]
						UpperCAmelCase_     : dict[int, list[int]]         =					{
						    1: [2, 3, 4],
						    2: [5],
						    3: [6, 7],
						    4: [8],
						    5: [9, 10],
						    6: [11],
						    7: [],
						    8: [12, 13],
						    9: [],
						    10: [],
						    11: [],
						    12: [],
						    13: [],
						}
						UpperCAmelCase_  ,    UpperCAmelCase_     : List[str]         =					breadth_first_search(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__,     1				)
						UpperCAmelCase_     : Optional[int]         =					create_sparse(SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)
						print('''LCA of node 1 and 3 is: ''',     lowest_common_ancestor(1,     3,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)
						print('''LCA of node 5 and 6 is: ''',     lowest_common_ancestor(5,     6,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)
						print('''LCA of node 7 and 11 is: ''',     lowest_common_ancestor(7,     11,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)
						print('''LCA of node 6 and 7 is: ''',     lowest_common_ancestor(6,     7,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)
						print('''LCA of node 4 and 12 is: ''',     lowest_common_ancestor(4,     12,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)
						print('''LCA of node 8 and 8 is: ''',     lowest_common_ancestor(8,     8,     SCREAMING_SNAKE_CASE__,     SCREAMING_SNAKE_CASE__				)				)


if __name__ == "__main__":
					main()












'''simple docstring'''







from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import PNDMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


class    __a (lowerCamelCase       ):
							__a   :				UNetaDModel
							__a   :				PNDMScheduler

							def __init__(							self							:       Optional[Any]    ,       __magic_name__							:       UNetaDModel    ,       __magic_name__							:       PNDMScheduler				)   ->    Tuple:







													"""simple docstring"""
													super().__init__()

													UpperCAmelCase_     : Optional[int]         =					PNDMScheduler.from_config(scheduler.config				)

													self.register_modules(unet=__magic_name__    ,       scheduler=__magic_name__				)



							@torch.no_grad()
							def __call__(							self							:       Union[str, Any]    ,       __magic_name__							:       int = 1    ,       __magic_name__							:       int = 50    ,       __magic_name__							:       Optional[Union[torch.Generator, List[torch.Generator]]] = None    ,       __magic_name__							:       Optional[str] = "pil"    ,       __magic_name__							:       bool = True    ,       **__magic_name__							:       Dict    ,       )   ->    Union[ImagePipelineOutput, Tuple]:







													"""simple docstring"""
													UpperCAmelCase_     : Dict         =					randn_tensor(
													    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)    ,       generator=__magic_name__    ,       device=self.device    ,       )

													self.scheduler.set_timesteps(__magic_name__				)
													for t in self.progress_bar(self.scheduler.timesteps				):
																			UpperCAmelCase_     : Optional[int]         =					self.unet(__magic_name__    ,       __magic_name__				).sample

																			UpperCAmelCase_     : str         =					self.scheduler.step(__magic_name__    ,       __magic_name__    ,       __magic_name__				).prev_sample

													UpperCAmelCase_     : int         =					(image / 2 + 0.5).clamp(0    ,       1				)
													UpperCAmelCase_     : Any         =					image.cpu().permute(0    ,       2    ,       3    ,       1				).numpy()
													if output_type == "pil":
																			UpperCAmelCase_     : Optional[int]         =					self.numpy_to_pil(__magic_name__				)

													if not return_dict:
																			return (image,)

													return ImagePipelineOutput(images=__magic_name__				)





