
'''simple docstring'''




from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


lowercase			:				int    		=			8







def 		lowerCAmelCase_				(   snake_case__		,				snake_case__=BITS						):




    '''simple docstring'''



    A       :   Optional[Any]					=						x.device

    A       :   Optional[Any]					=						(x * 255).int().clamp(0		,				255						)

    A       :   Union[str, Any]					=						2 ** torch.arange(bits - 1		,				-1		,				-1		,				device=snake_case__						)
    A       :   int					=						rearrange(snake_case__		,				'''d -> d 1 1'''						)
    A       :   Optional[Any]					=						rearrange(snake_case__		,				'''b c h w -> b c 1 h w'''						)

    A       :   Union[str, Any]					=						((x & mask) != 0).float()
    A       :   int					=						rearrange(snake_case__		,				'''b c d h w -> b (c d) h w'''						)
    A       :   Any					=						bits * 2 - 1
    return bits







def 		lowerCAmelCase_				(   snake_case__		,				snake_case__=BITS						):




    '''simple docstring'''



    A       :   Any					=						x.device

    A       :   List[str]					=						(x > 0).int()
    A       :   str					=						2 ** torch.arange(bits - 1		,				-1		,				-1		,				device=snake_case__		,				dtype=torch.intaa						)

    A       :   Union[str, Any]					=						rearrange(snake_case__		,				'''d -> d 1 1'''						)
    A       :   Tuple					=						rearrange(snake_case__		,				'''b (c d) h w -> b c d h w'''		,				d=8						)
    A       :   int					=						reduce(x * mask		,				'''b c d h w -> b c h w'''		,				'''sum'''						)
    return (dec / 255).clamp(0.0		,				1.0						)







def 		lowerCAmelCase_				(   self		,				snake_case__		,				snake_case__		,				snake_case__		,				snake_case__ = 0.0		,				snake_case__ = True		,				snake_case__=None		,				snake_case__ = True		,				):




    '''simple docstring'''



    if self.num_inference_steps is None:
        raise ValueError(
            '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''						)

    # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
    # Ideally, read DDIM paper in-detail understanding

    # Notation (<variable name> -> <name in paper>
    # - pred_noise_t -> e_theta(x_t, t)
    # - pred_original_sample -> f_theta(x_t, t) or x_0
    # - std_dev_t -> sigma_t
    # - eta -> η
    # - pred_sample_direction -> "direction pointing to x_t"
    # - pred_prev_sample -> "x_t-1"

    # 1. get previous step value (=t-1)
    A       :   Union[str, Any]					=						timestep - self.config.num_train_timesteps // self.num_inference_steps

    # 2. compute alphas, betas
    A       :   str					=						self.alphas_cumprod[timestep]
    A       :   Any					=						self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

    A       :   int					=						1 - alpha_prod_t

    # 3. compute predicted original sample from predicted noise also called
    # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
    A       :   Union[str, Any]					=						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

    # 4. Clip "predicted x_0"
    A       :   Optional[Any]					=						self.bit_scale
    if self.config.clip_sample:
        A       :   Union[str, Any]					=						torch.clamp(snake_case__		,				-scale		,				snake_case__						)

    # 5. compute variance: "sigma_t(η)" -> see formula (16)
    # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
    A       :   Optional[Any]					=						self._get_variance(snake_case__		,				snake_case__						)
    A       :   Optional[int]					=						eta * variance ** 0.5

    if use_clipped_model_output:
        # the model_output is always re-derived from the clipped x_0 in Glide
        A       :   Union[str, Any]					=						(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

    # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
    A       :   List[Any]					=						(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

    # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
    A       :   Optional[Any]					=						alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

    if eta > 0:
        # randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
        A       :   Dict					=						model_output.device if torch.is_tensor(snake_case__						) else '''cpu'''
        A       :   Optional[Any]					=						torch.randn(model_output.shape		,				dtype=model_output.dtype		,				generator=snake_case__						).to(snake_case__						)
        A       :   int					=						self._get_variance(snake_case__		,				snake_case__						) ** 0.5 * eta * noise

        A       :   List[str]					=						prev_sample + variance

    if not return_dict:
        return (prev_sample,)

    return DDIMSchedulerOutput(prev_sample=snake_case__		,				pred_original_sample=snake_case__						)







def 		lowerCAmelCase_				(   self		,				snake_case__		,				snake_case__		,				snake_case__		,				snake_case__="epsilon"		,				snake_case__=None		,				snake_case__ = True		,				):




    '''simple docstring'''



    A       :   Dict					=						timestep

    if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
        A,  A       :   int					=						torch.split(snake_case__		,				sample.shape[1]		,				dim=1						)
    else:
        A       :   Any					=						None

    # 1. compute alphas, betas
    A       :   int					=						self.alphas_cumprod[t]
    A       :   Any					=						self.alphas_cumprod[t - 1] if t > 0 else self.one
    A       :   Union[str, Any]					=						1 - alpha_prod_t
    A       :   int					=						1 - alpha_prod_t_prev

    # 2. compute predicted original sample from predicted noise also called
    # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
    if prediction_type == "epsilon":
        A       :   Union[str, Any]					=						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
    elif prediction_type == "sample":
        A       :   str					=						model_output
    else:
        raise ValueError(F'Unsupported prediction_type {prediction_type}.'						)

    # 3. Clip "predicted x_0"
    A       :   Optional[int]					=						self.bit_scale
    if self.config.clip_sample:
        A       :   Any					=						torch.clamp(snake_case__		,				-scale		,				snake_case__						)

    # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
    # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    A       :   Optional[Any]					=						(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
    A       :   List[str]					=						self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

    # 5. Compute predicted previous sample µ_t
    # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
    A       :   Union[str, Any]					=						pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

    # 6. Add noise
    A       :   int					=						0
    if t > 0:
        A       :   Tuple					=						torch.randn(
            model_output.size()		,				dtype=model_output.dtype		,				layout=model_output.layout		,				generator=snake_case__						).to(model_output.device						)
        A       :   str					=						(self._get_variance(snake_case__		,				predicted_variance=snake_case__						) ** 0.5) * noise

    A       :   Dict					=						pred_prev_sample + variance

    if not return_dict:
        return (pred_prev_sample,)

    return DDPMSchedulerOutput(prev_sample=snake_case__		,				pred_original_sample=snake_case__						)







class  A				(							__snake_case						):





     def __init__(							self						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE = 1.0						,			) ->				Dict:






         """simple docstring"""






         super().__init__()
         A       :   Optional[int]					=						bit_scale
         A       :   str					=						(
             ddim_bit_scheduler_step if isinstance(SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	) else ddpm_bit_scheduler_step
         )

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





     @torch.no_grad()
     def __call__(							self						,			SCREAMING_SNAKE_CASE = 256						,			SCREAMING_SNAKE_CASE = 256						,			SCREAMING_SNAKE_CASE = 50						,			SCREAMING_SNAKE_CASE = None						,			SCREAMING_SNAKE_CASE = 1						,			SCREAMING_SNAKE_CASE = "pil"						,			SCREAMING_SNAKE_CASE = True						,			**SCREAMING_SNAKE_CASE						,			) ->				Union[Tuple, ImagePipelineOutput]:






         """simple docstring"""






         A       :   List[Any]					=						torch.randn(
             (batch_size, self.unet.config.in_channels, height, width)						,			generator=SCREAMING_SNAKE_CASE						,			)
         A       :   Tuple					=						decimal_to_bits(SCREAMING_SNAKE_CASE	) * self.bit_scale
         A       :   str					=						latents.to(self.device	)

         self.scheduler.set_timesteps(SCREAMING_SNAKE_CASE	)

         for t in self.progress_bar(self.scheduler.timesteps	):
             # predict the noise residual
             A       :   Any					=						self.unet(SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	).sample

             # compute the previous noisy sample x_t -> x_t-1
             A       :   Union[str, Any]					=						self.scheduler.step(SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	).prev_sample

         A       :   List[Any]					=						bits_to_decimal(SCREAMING_SNAKE_CASE	)

         if output_type == "pil":
             A       :   Any					=						self.numpy_to_pil(SCREAMING_SNAKE_CASE	)

         if not return_dict:
             return (image,)

         return ImagePipelineOutput(images=SCREAMING_SNAKE_CASE	)






'''simple docstring'''




class  A				:





     def __init__(							self						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	) ->				Tuple:






         """simple docstring"""






         A       :   Any					=						None
         A       :   Optional[Any]					=						None
         A       :   Tuple					=						graph

         self._normalize_graph(SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	)
         A       :   Dict					=						len(SCREAMING_SNAKE_CASE	)
         A       :   Optional[Any]					=						None





     def 				__lowerCAmelCase							(							self						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	) ->				List[Any]:






         """simple docstring"""






         if sources is int:
             A       :   Dict					=						[sources]
         if sinks is int:
             A       :   str					=						[sinks]

         if len(SCREAMING_SNAKE_CASE	) == 0 or len(SCREAMING_SNAKE_CASE	) == 0:
             return

         A       :   Optional[int]					=						sources[0]
         A       :   Union[str, Any]					=						sinks[0]

         # make fake vertex if there are more
         # than one source or sink
         if len(SCREAMING_SNAKE_CASE	) > 1 or len(SCREAMING_SNAKE_CASE	) > 1:
             A       :   Optional[int]					=						0
             for i in sources:
                 max_input_flow += sum(self.graph[i]	)

             A       :   Dict					=						len(self.graph	) + 1
             for room in self.graph:
                 room.insert(0						,			0	)
             self.graph.insert(0						,			[0] * size	)
             for i in sources:
                 A       :   Dict					=						max_input_flow
             A       :   Tuple					=						0

             A       :   Tuple					=						len(self.graph	) + 1
             for room in self.graph:
                 room.append(0	)
             self.graph.append([0] * size	)
             for i in sinks:
                 A       :   Optional[Any]					=						max_input_flow
             A       :   Optional[Any]					=						size - 1





     def 				__lowerCAmelCase							(							self	) ->				Any:






         """simple docstring"""






         if self.maximum_flow_algorithm is None:
             raise Exception('''You need to set maximum flow algorithm before.'''	)
         if self.source_index is None or self.sink_index is None:
             return 0

         self.maximum_flow_algorithm.execute()
         return self.maximum_flow_algorithm.getMaximumFlow()





     def 				__lowerCAmelCase							(							self						,			SCREAMING_SNAKE_CASE	) ->				Union[str, Any]:






         """simple docstring"""






         A       :   List[Any]					=						algorithm(self	)





class  A				:





     def __init__(							self						,			SCREAMING_SNAKE_CASE	) ->				Union[str, Any]:






         """simple docstring"""






         A       :   Union[str, Any]					=						flow_network
         A       :   Optional[Any]					=						flow_network.verticesCount
         A       :   Tuple					=						flow_network.sourceIndex
         A       :   Dict					=						flow_network.sinkIndex
         # it's just a reference, so you shouldn't change
         # it in your algorithms, use deep copy before doing that
         A       :   str					=						flow_network.graph
         A       :   Optional[Any]					=						False





     def 				__lowerCAmelCase							(							self	) ->				Optional[int]:






         """simple docstring"""






         if not self.executed:
             self._algorithm()
             A       :   Optional[int]					=						True





     def 				__lowerCAmelCase							(							self	) ->				Any:






         """simple docstring"""






         pass





class  A				(							__snake_case						):





     def __init__(							self						,			SCREAMING_SNAKE_CASE	) ->				Dict:






         """simple docstring"""






         super().__init__(SCREAMING_SNAKE_CASE	)
         # use this to save your result
         A       :   List[str]					=						-1





     def 				__lowerCAmelCase							(							self	) ->				str:






         """simple docstring"""






         if not self.executed:
             raise Exception('''You should execute algorithm before using its result!'''	)

         return self.maximum_flow





class  A				(							__snake_case						):





     def __init__(							self						,			SCREAMING_SNAKE_CASE	) ->				List[Any]:






         """simple docstring"""






         super().__init__(SCREAMING_SNAKE_CASE	)

         A       :   Optional[Any]					=						[[0] * self.verticies_count for i in range(self.verticies_count	)]

         A       :   Union[str, Any]					=						[0] * self.verticies_count
         A       :   List[Any]					=						[0] * self.verticies_count





     def 				__lowerCAmelCase							(							self	) ->				Dict:






         """simple docstring"""






         A       :   Tuple					=						self.verticies_count

         # push some substance to graph
         for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]	):
             self.preflow[self.source_index][nextvertex_index] += bandwidth
             self.preflow[nextvertex_index][self.source_index] -= bandwidth
             self.excesses[nextvertex_index] += bandwidth

         # Relabel-to-front selection rule
         A       :   Optional[Any]					=						[
             i
             for i in range(self.verticies_count	)
             if i != self.source_index and i != self.sink_index
         ]

         # move through list
         A       :   Union[str, Any]					=						0
         while i < len(SCREAMING_SNAKE_CASE	):
             A       :   str					=						vertices_list[i]
             A       :   List[str]					=						self.heights[vertex_index]
             self.process_vertex(SCREAMING_SNAKE_CASE	)
             if self.heights[vertex_index] > previous_height:
                 # if it was relabeled, swap elements
                 # and start from 0 index
                 vertices_list.insert(0						,			vertices_list.pop(SCREAMING_SNAKE_CASE	)	)
                 A       :   int					=						0
             else:
                 i += 1

         A       :   Optional[Any]					=						sum(self.preflow[self.source_index]	)





     def 				__lowerCAmelCase							(							self						,			SCREAMING_SNAKE_CASE	) ->				Tuple:






         """simple docstring"""






         while self.excesses[vertex_index] > 0:
             for neighbour_index in range(self.verticies_count	):
                 # if it's neighbour and current vertex is higher
                 if (
                     self.graph[vertex_index][neighbour_index]
                     - self.preflow[vertex_index][neighbour_index]
                     > 0
                     and self.heights[vertex_index] > self.heights[neighbour_index]
                 ):
                     self.push(SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	)

             self.relabel(SCREAMING_SNAKE_CASE	)





     def 				__lowerCAmelCase							(							self						,			SCREAMING_SNAKE_CASE						,			SCREAMING_SNAKE_CASE	) ->				Union[str, Any]:






         """simple docstring"""






         A       :   Dict					=						min(
             self.excesses[from_index]						,			self.graph[from_index][to_index] - self.preflow[from_index][to_index]						,			)
         self.preflow[from_index][to_index] += preflow_delta
         self.preflow[to_index][from_index] -= preflow_delta
         self.excesses[from_index] -= preflow_delta
         self.excesses[to_index] += preflow_delta





     def 				__lowerCAmelCase							(							self						,			SCREAMING_SNAKE_CASE	) ->				int:






         """simple docstring"""






         A       :   Dict					=						None
         for to_index in range(self.verticies_count	):
             if (
                 self.graph[vertex_index][to_index]
                 - self.preflow[vertex_index][to_index]
                 > 0
             ) and (min_height is None or self.heights[to_index] < min_height):
                 A       :   Dict					=						self.heights[to_index]

         if min_height is not None:
             A       :   Dict					=						min_height + 1


if __name__ == "__main__":
      lowercase			:				Optional[int]    		=			[0]
      lowercase			:				List[Any]    		=			[3]
      # graph = [
      #     [0, 0, 4, 6, 0, 0],
      #     [0, 0, 5, 2, 0, 0],
      #     [0, 0, 0, 0, 4, 4],
      #     [0, 0, 0, 0, 6, 6],
      #     [0, 0, 0, 0, 0, 0],
      #     [0, 0, 0, 0, 0, 0],
      # ]
      lowercase			:				int    		=			[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

      # prepare our network
      lowercase			:				List[str]    		=			FlowNetwork(graph, entrances, exits)
      # set algorithm
      flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
      # and calculate
      lowercase			:				List[str]    		=			flow_network.find_maximum_flow()

      print(f'''maximum flow is {maximum_flow}''')




