






# using dfs for finding eulerian path traversal





def 					lowercase_ (    __snake_case     :							int	,	__snake_case     :							int	,	__snake_case     :							int	,	__snake_case     :							Tuple=None      )     -> Dict:





				'''simple docstring'''


				snake_case__      :int         =   (path or []) + [u]
				for v in graph[u]:
								if visited_edge[u][v] is False:
												snake_case__    ,						snake_case__      :Optional[int]         =   True, True
												snake_case__      :List[Any]         =   dfs(__snake_case	,	__snake_case	,	__snake_case	,	__snake_case      )
				return path





def 					lowercase_ (    __snake_case     :							Dict	,	__snake_case     :							int      )     -> Optional[Any]:





				'''simple docstring'''


				snake_case__      :Any         =   0
				snake_case__      :Union[str, Any]         =   -1
				for i in range(__snake_case      ):
								if i not in graph.keys():
												continue
								if len(graph[i]      ) % 2 == 1:
												odd_degree_nodes += 1
												snake_case__      :Any         =   i
				if odd_degree_nodes == 0:
								return 1, odd_node
				if odd_degree_nodes == 2:
								return 2, odd_node
				return 3, odd_node





def 					lowercase_ (    __snake_case     :							int	,	__snake_case     :							Union[str, Any]      )     -> Any:





				'''simple docstring'''


				snake_case__      :str         =   [[False for _ in range(max_node + 1      )] for _ in range(max_node + 1      )]
				snake_case__    ,						snake_case__      :Tuple         =   check_circuit_or_path(__snake_case	,	__snake_case      )
				if check == 3:
								print("graph is not Eulerian"      )
								print("no path"      )
								return
				snake_case__      :Tuple         =   1
				if check == 2:
								snake_case__      :Union[str, Any]         =   odd_node
								print("graph has a Euler path"      )
				if check == 1:
								print("graph has a Euler cycle"      )
				snake_case__      :str         =   dfs(__snake_case	,	__snake_case	,	__snake_case      )
				print(__snake_case      )





def 					lowercase_ (    )     -> Any:





				'''simple docstring'''


				snake_case__      :Tuple         =   {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
				snake_case__      :Tuple         =   {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
				snake_case__      :Optional[int]         =   {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
				snake_case__      :Union[str, Any]         =   {1: [2, 3], 2: [1, 3], 3: [1, 2]}
				snake_case__      :Tuple         =   {
				    1: [],
				    2: []
				    # all degree is zero
				}
				snake_case__      :List[Any]         =   10
				check_euler(__snake_case	,	__snake_case      )
				check_euler(__snake_case	,	__snake_case      )
				check_euler(__snake_case	,	__snake_case      )
				check_euler(__snake_case	,	__snake_case      )
				check_euler(__snake_case	,	__snake_case      )


if __name__ == "__main__":
	main()







from ...utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_torch_available,
    is_transformers_available,
)


try:
	if not (is_transformers_available() and is_torch_available()):
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
	from .multicontrolnet import MultiControlNetModel
	from .pipeline_controlnet import StableDiffusionControlNetPipeline
	from .pipeline_controlnet_imgaimg import StableDiffusionControlNetImgaImgPipeline
	from .pipeline_controlnet_inpaint import StableDiffusionControlNetInpaintPipeline


if is_transformers_available() and is_flax_available():
	from .pipeline_flax_controlnet import FlaxStableDiffusionControlNetPipeline