


def 	_lowerCAmelCase					( UpperCamelCase__:  List[Any]				,       UpperCamelCase__:  Optional[int]				,       UpperCamelCase__:  List[Any]    )			-> bool:





	"""simple docstring"""







	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(UpperCamelCase__    )    )





def 	_lowerCAmelCase					( UpperCamelCase__:  Dict				,       UpperCamelCase__:  List[str]				,       UpperCamelCase__:  str				,       UpperCamelCase__:  List[str]    )			-> bool:





	"""simple docstring"""







	if index == len(UpperCamelCase__    ):
		return True

	# Recursive Step
	for i in range(UpperCamelCase__    ):
		if valid_coloring(graph[index]				,       UpperCamelCase__				,       UpperCamelCase__    ):
			# Color current vertex
			A             =					i
			# Validate coloring
			if util_color(UpperCamelCase__				,       UpperCamelCase__				,       UpperCamelCase__				,       index + 1    ):
				return True
			# Backtrack
			A             =					-1
	return False





def 	_lowerCAmelCase					( UpperCamelCase__:  Any				,       UpperCamelCase__:  Tuple    )			-> list[int]:





	"""simple docstring"""







	A             =					[-1] * len(UpperCamelCase__    )

	if util_color(UpperCamelCase__				,       UpperCamelCase__				,       UpperCamelCase__				,       0    ):
		return colored_vertices

	return []






"""simple docstring"""
# limitations under the License.

# NOTE: This file is deprecated and will be removed in a future version.
# It only exists so that temporarely `from diffusers.pipelines import DiffusionPipeline` works

from .pipelines import DiffusionPipeline, ImagePipelineOutput  # noqa: F401
from .utils import deprecate


deprecate(
    """pipelines_utils""",
    """0.22.0""",
    """Importing `DiffusionPipeline` or `ImagePipelineOutput` from diffusers.pipeline_utils is deprecated. Please import from diffusers.pipelines.pipeline_utils instead.""",
    standard_warn=False,
    stacklevel=3,
)

