
def 	A_ (							snake_case							:   int )      ->    None:



						'''simple docstring'''

						__UpperCamelCase       =			generate_pascal_triangle(snake_case )
						for row_idx in range(snake_case ):
												# Print left spaces
												for _ in range(num_rows - row_idx - 1 ):
																		print(end=''' ''' )
												# Print row values
												for col_idx in range(row_idx + 1 ):
																		if col_idx != row_idx:
																								print(triangle[row_idx][col_idx] ,      end=''' ''' )
																		else:
																								print(triangle[row_idx][col_idx] ,      end='''''' )
												print()




def 	A_ (							snake_case							:   int )      ->    list[list[int]]:



						'''simple docstring'''

						if not isinstance(snake_case ,      snake_case ):
												raise TypeError('''The input value of \'num_rows\' should be \'int\'''' )

						if num_rows == 0:
												return []
						elif num_rows < 0:
												raise ValueError(
												    '''The input value of \'num_rows\' should be greater than or equal to 0''' )

						__UpperCamelCase       =			[]
						for current_row_idx in range(snake_case ):
												__UpperCamelCase       =			populate_current_row(snake_case ,      snake_case )
												triangle.append(snake_case )
						return triangle




def 	A_ (							snake_case							:   list[list[int]] ,      snake_case							:   int )      ->    list[int]:



						'''simple docstring'''

						__UpperCamelCase       =			[-1] * (current_row_idx + 1)
						# first and last elements of current row are equal to 1
						__UpperCamelCase  ,							__UpperCamelCase       =			1, 1
						for current_col_idx in range(1 ,      snake_case ):
												calculate_current_element(
												    snake_case ,      snake_case ,      snake_case ,      snake_case )
						return current_row




def 	A_ (							snake_case							:   list[list[int]] ,      snake_case							:   list[int] ,      snake_case							:   int ,      snake_case							:   int ,      )      ->    None:



						'''simple docstring'''

						__UpperCamelCase       =			triangle[current_row_idx - 1][current_col_idx - 1]
						__UpperCamelCase       =			triangle[current_row_idx - 1][current_col_idx]
						__UpperCamelCase       =			above_to_left_elt + above_to_right_elt




def 	A_ (							snake_case							:   int )      ->    list[list[int]]:



						'''simple docstring'''

						if not isinstance(snake_case ,      snake_case ):
												raise TypeError('''The input value of \'num_rows\' should be \'int\'''' )

						if num_rows == 0:
												return []
						elif num_rows < 0:
												raise ValueError(
												    '''The input value of \'num_rows\' should be greater than or equal to 0''' )

						__UpperCamelCase       =			[[1]]

						for row_index in range(1 ,      snake_case ):
												__UpperCamelCase       =			[0] + result[-1] + [0]
												__UpperCamelCase       =			row_index + 1
												# Calculate the number of distinct elements in a row
												__UpperCamelCase       =			sum(divmod(snake_case ,      2 ) )
												__UpperCamelCase       =			[
												    temp_row[i - 1] + temp_row[i] for i in range(1 ,      distinct_elements + 1 )
												]
												__UpperCamelCase       =			row_first_half[: (row_index + 1) // 2]
												row_second_half.reverse()
												__UpperCamelCase       =			row_first_half + row_second_half
												result.append(snake_case )

						return result




def 	A_ (							)      ->    None:



						'''simple docstring'''

						from collections.abc import Callable
						from timeit import timeit

						def benchmark_a_function(snake_case							:   Callable ,      snake_case							:   int ) -> None:
												__UpperCamelCase       =			f"{func.__name__}({value})"
												__UpperCamelCase       =			timeit(f"__main__.{call}" ,      setup='''import __main__''' )
												# print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
												print(f"{call:38} -- {timing:.4f} seconds" )

						for value in range(15 ):  # (1, 7, 14):
												for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
																		benchmark_a_function(snake_case ,      snake_case )
												print()


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				benchmark()






from typing import List, Optional, Tuple, Union

import torch

from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






class        SCREAMING_SNAKE_CASE__    (							SCREAMING_SNAKE_CASE_    ):

							"""simple docstring"""






							def __init__(  self     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			)->   str:





													'''simple docstring'''






													super().__init__()

													# make sure scheduler can always be converted to DDIM
													__UpperCamelCase       =			DDIMScheduler.from_config(scheduler.config			)

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



							@torch.no_grad()
							def __call__(  self     ,	SCREAMING_SNAKE_CASE_ = 1     ,	SCREAMING_SNAKE_CASE_ = None     ,	SCREAMING_SNAKE_CASE_ = 0.0     ,	SCREAMING_SNAKE_CASE_ = 50     ,	SCREAMING_SNAKE_CASE_ = None     ,	SCREAMING_SNAKE_CASE_ = "pil"     ,	SCREAMING_SNAKE_CASE_ = True     ,	)->   Union[ImagePipelineOutput, Tuple]:





													'''simple docstring'''






													if isinstance(self.unet.config.sample_size     ,	SCREAMING_SNAKE_CASE_			):
																			__UpperCamelCase       =			(
																			    batch_size,
																			    self.unet.config.in_channels,
																			    self.unet.config.sample_size,
																			    self.unet.config.sample_size,
																			)
													else:
																			__UpperCamelCase       =			(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

													if isinstance(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			) and len(SCREAMING_SNAKE_CASE_			) != batch_size:
																			raise ValueError(
																			    F"You have passed a list of generators of length {len(SCREAMING_SNAKE_CASE_			)}, but requested an effective batch"
																			    F" size of {batch_size}. Make sure the batch size matches the length of the generators."			)

													__UpperCamelCase       =			randn_tensor(SCREAMING_SNAKE_CASE_     ,	generator=SCREAMING_SNAKE_CASE_     ,	device=self.device     ,	dtype=self.unet.dtype			)

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

													for t in self.progress_bar(self.scheduler.timesteps			):
																			# 1. predict noise model_output
																			__UpperCamelCase       =			self.unet(SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_			).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
																			__UpperCamelCase       =			self.scheduler.step(
																			    SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	SCREAMING_SNAKE_CASE_     ,	eta=SCREAMING_SNAKE_CASE_     ,	use_clipped_model_output=SCREAMING_SNAKE_CASE_     ,	generator=SCREAMING_SNAKE_CASE_			).prev_sample

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

													if not return_dict:
																			return (image,)

													return ImagePipelineOutput(images=SCREAMING_SNAKE_CASE_			)




