

from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
__A   :     int      =			{
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}
def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> List[Any]:



				'''simple docstring'''






				lowerCAmelCase				:			Any    			=      {node: {node} for node in graph}

				lowerCAmelCase				:			Optional[int]    			=      {node: graph[node][:] for node in graph}

				while len(_UpperCAmelCase				) > 2:
								# Choose a random edge.
								lowerCAmelCase				:			Tuple    			=      random.choice(list(graph_copy.keys()				)				)
								lowerCAmelCase				:			Union[str, Any]    			=      random.choice(graph_copy[u]				)

								# Contract edge (u, v) to new node uv
								lowerCAmelCase				:			List[str]    			=      u + v
								lowerCAmelCase				:			int    			=      list(set(graph_copy[u] + graph_copy[v]				)				)
								uv_neighbors.remove(_UpperCAmelCase				)
								uv_neighbors.remove(_UpperCAmelCase				)
								lowerCAmelCase				:			Tuple    			=      uv_neighbors
								for neighbor in uv_neighbors:
												graph_copy[neighbor].append(_UpperCAmelCase				)

								lowerCAmelCase				:			Optional[Any]    			=      set(contracted_nodes[u].union(contracted_nodes[v]				)				)

								# Remove nodes u and v.
								del graph_copy[u]
								del graph_copy[v]
								for neighbor in uv_neighbors:
												if u in graph_copy[neighbor]:
																graph_copy[neighbor].remove(_UpperCAmelCase				)
												if v in graph_copy[neighbor]:
																graph_copy[neighbor].remove(_UpperCAmelCase				)

    # Find cutset.
				lowerCAmelCase				:			Any    			=      [contracted_nodes[node] for node in graph_copy]
				return {
				    (node, neighbor)
				    for node in groups[0]
				    for neighbor in graph[node]
				    if neighbor in groups[1]
				}


if __name__ == "__main__":
	print(partition_graph(TEST_GRAPH))








import torch

from diffusers import KDPMaAncestralDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class    __A				(							lowerCAmelCase ):
    lowerCAmelCase_							:		List[str]						=							(KDPMaAncestralDiscreteScheduler,)
    lowerCAmelCase_							:		Dict						=							10






    def 	lowercase__ (	self			:    Any    ,				**UpperCAmelCase_			:    List[Any]    ):
        lowerCAmelCase				:			int    			=      {
            'num_train_timesteps': 1100,
            'beta_start': 0.00_01,
            'beta_end': 0.02,
            'beta_schedule': 'linear',
        }

        config.update(**UpperCAmelCase_    )
        return config






    def 	lowercase__ (	self			:    Optional[Any]    ):
        for timesteps in [10, 50, 100, 1000]:
            self.check_over_configs(num_train_timesteps=UpperCAmelCase_    )






    def 	lowercase__ (	self			:    List[str]    ):
        for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]    ,				[0.00_02, 0.0_02, 0.02]    ):
            self.check_over_configs(beta_start=UpperCAmelCase_    ,				beta_end=UpperCAmelCase_    )






    def 	lowercase__ (	self			:    Optional[int]    ):
        for schedule in ["linear", "scaled_linear"]:
            self.check_over_configs(beta_schedule=UpperCAmelCase_    )






    def 	lowercase__ (	self			:    int    ):
        if torch_device == "mps":
            return
        lowerCAmelCase				:			Any    			=      self.scheduler_classes[0]
        lowerCAmelCase				:			Optional[int]    			=      self.get_scheduler_config()
        lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )

        scheduler.set_timesteps(self.num_inference_steps    )

        lowerCAmelCase				:			Any    			=      torch.manual_seed(0    )

        lowerCAmelCase				:			List[Any]    			=      self.dummy_model()
        lowerCAmelCase				:			List[Any]    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
        lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )

        for i, t in enumerate(scheduler.timesteps    ):
            lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			Any    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			Optional[Any]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
            lowerCAmelCase				:			Union[str, Any]    			=      output.prev_sample

        lowerCAmelCase				:			List[Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
        lowerCAmelCase				:			Any    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )

        assert abs(result_sum.item() - 1_38_49.38_77    ) < 1E-2
        assert abs(result_mean.item() - 18.03_31    ) < 5E-3






    def 	lowercase__ (	self			:    Tuple    ):
        for prediction_type in ["epsilon", "v_prediction"]:
            self.check_over_configs(prediction_type=UpperCAmelCase_    )






    def 	lowercase__ (	self			:    List[str]    ):
        if torch_device == "mps":
            return
        lowerCAmelCase				:			Optional[Any]    			=      self.scheduler_classes[0]
        lowerCAmelCase				:			List[Any]    			=      self.get_scheduler_config(prediction_type='v_prediction'    )
        lowerCAmelCase				:			Any    			=      scheduler_class(**UpperCAmelCase_    )

        scheduler.set_timesteps(self.num_inference_steps    )

        lowerCAmelCase				:			Optional[int]    			=      self.dummy_model()
        lowerCAmelCase				:			Any    			=      self.dummy_sample_deter * scheduler.init_noise_sigma
        lowerCAmelCase				:			Optional[int]    			=      sample.to(UpperCAmelCase_    )

        lowerCAmelCase				:			Optional[int]    			=      torch.manual_seed(0    )

        for i, t in enumerate(scheduler.timesteps    ):
            lowerCAmelCase				:			Dict    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			Optional[int]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			Optional[int]    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
            lowerCAmelCase				:			str    			=      output.prev_sample

        lowerCAmelCase				:			str    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
        lowerCAmelCase				:			Tuple    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )

        assert abs(result_sum.item() - 3_28.99_70    ) < 1E-2
        assert abs(result_mean.item() - 0.42_84    ) < 1E-3






    def 	lowercase__ (	self			:    Tuple    ):
        if torch_device == "mps":
            return
        lowerCAmelCase				:			str    			=      self.scheduler_classes[0]
        lowerCAmelCase				:			Dict    			=      self.get_scheduler_config()
        lowerCAmelCase				:			List[str]    			=      scheduler_class(**UpperCAmelCase_    )

        scheduler.set_timesteps(self.num_inference_steps    ,				device=UpperCAmelCase_    )
        lowerCAmelCase				:			int    			=      torch.manual_seed(0    )

        lowerCAmelCase				:			Tuple    			=      self.dummy_model()
        lowerCAmelCase				:			Optional[Any]    			=      self.dummy_sample_deter.to(UpperCAmelCase_    ) * scheduler.init_noise_sigma

        for t in scheduler.timesteps:
            lowerCAmelCase				:			str    			=      scheduler.scale_model_input(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			List[Any]    			=      model(UpperCAmelCase_    ,				UpperCAmelCase_    )

            lowerCAmelCase				:			Dict    			=      scheduler.step(UpperCAmelCase_    ,				UpperCAmelCase_    ,				UpperCAmelCase_    ,				generator=UpperCAmelCase_    )
            lowerCAmelCase				:			Dict    			=      output.prev_sample

        lowerCAmelCase				:			Union[str, Any]    			=      torch.sum(torch.abs(UpperCAmelCase_    )    )
        lowerCAmelCase				:			str    			=      torch.mean(torch.abs(UpperCAmelCase_    )    )

        assert abs(result_sum.item() - 1_38_49.38_18    ) < 1E-1
        assert abs(result_mean.item() - 18.03_31    ) < 1E-3





