



def 	_lowerCAmelCase						(				__lowerCamelCase   :     list[int]		,	__lowerCamelCase   :     list[int]		,	__lowerCamelCase   :     int     ):



 """simple docstring"""





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






def 	_lowerCAmelCase						(				__lowerCamelCase   :     list[list[int]]		,	__lowerCamelCase   :     int		,	__lowerCamelCase   :     list[int]		,	__lowerCamelCase   :     int     ):



 """simple docstring"""





 if index == len(__lowerCamelCase     ):
  return True

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






def 	_lowerCAmelCase						(				__lowerCamelCase   :     list[list[int]]		,	__lowerCamelCase   :     int     ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE       :    Optional[int]       =	[-1] * len(__lowerCamelCase     )

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

 return []











from abc import ABC, abstractmethod
from typing import Optional, Union

from .. import Dataset, DatasetDict, Features, IterableDataset, IterableDatasetDict, NamedSplit
from ..utils.typing import NestedDataStructureLike, PathLike

class       _SCREAMING_SNAKE_CASE	(UpperCamelCase ):





     def __init__(       self :							List[str]     ,  UpperCamelCase :							Optional[NestedDataStructureLike[PathLike]] = None     ,  UpperCamelCase :							Optional[NamedSplit] = None     ,  UpperCamelCase :							Optional[Features] = None     ,  UpperCamelCase :							str = None     ,  UpperCamelCase :							bool = False     ,  UpperCamelCase :							bool = False     ,  UpperCamelCase :							Optional[int] = None     ,  **UpperCamelCase :							Dict     ,  )->int:
      __SCREAMING_SNAKE_CASE       :    List[str]       =	path_or_paths
      __SCREAMING_SNAKE_CASE       :    Optional[int]       =	split if split or isinstance(UpperCamelCase     ,  UpperCamelCase				) else "train"
      __SCREAMING_SNAKE_CASE       :    Dict       =	features
      __SCREAMING_SNAKE_CASE       :    List[Any]       =	cache_dir
      __SCREAMING_SNAKE_CASE       :    Tuple       =	keep_in_memory
      __SCREAMING_SNAKE_CASE       :    Optional[Any]       =	streaming
      __SCREAMING_SNAKE_CASE       :    Optional[Any]       =	num_proc
      __SCREAMING_SNAKE_CASE       :    int       =	kwargs






     @abstractmethod
     def 	__snake_case    (       self :							Optional[int]				)->Union[Dataset, DatasetDict, IterableDataset, IterableDatasetDict]:
      pass






class       _SCREAMING_SNAKE_CASE	(UpperCamelCase ):





     def __init__(       self :							Optional[Any]     ,  UpperCamelCase :							Optional[Features] = None     ,  UpperCamelCase :							str = None     ,  UpperCamelCase :							bool = False     ,  UpperCamelCase :							bool = False     ,  UpperCamelCase :							Optional[int] = None     ,  **UpperCamelCase :							Dict     ,  )->Optional[int]:
      __SCREAMING_SNAKE_CASE       :    Optional[Any]       =	features
      __SCREAMING_SNAKE_CASE       :    str       =	cache_dir
      __SCREAMING_SNAKE_CASE       :    Any       =	keep_in_memory
      __SCREAMING_SNAKE_CASE       :    Optional[Any]       =	streaming
      __SCREAMING_SNAKE_CASE       :    int       =	num_proc
      __SCREAMING_SNAKE_CASE       :    Optional[Any]       =	kwargs






     @abstractmethod
     def 	__snake_case    (       self :							str				)->Union[Dataset, IterableDataset]:
      pass






