




'''simple docstring'''

# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.


def 		__magic_name__    (	__UpperCAmelCase	)		->					Optional[Any]:

					'''simple docstring'''

					snake_case_									=				[False] * len(__UpperCAmelCase	)
					snake_case_									=				[-1] * len(__UpperCAmelCase	)

					def dfs(__UpperCAmelCase,      __UpperCAmelCase	):
										snake_case_									=				True
										snake_case_									=				c
										for u in graph[v]:
															if not visited[u]:
																				dfs(__UpperCAmelCase,      1 - c	)

					for i in range(len(__UpperCAmelCase	)	):
										if not visited[i]:
															dfs(__UpperCAmelCase,      0	)

					for i in range(len(__UpperCAmelCase	)	):
										for j in graph[i]:
															if color[i] == color[j]:
																				return False

					return True


# Adjacency list of graph
a  :				Tuple									=  {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}

print(check_bipartite_dfs(graph))







'''simple docstring'''

from ..utils import DummyObject, requires_backends






class 						a				(   metaclass=_lowerCamelCase     ):
				snake_case_      =		["transformers", "torch", "note_seq"]


				def __init__(		self    :					Union[str, Any]       ,				*lowercase_    :					Optional[int]       ,				**lowercase_    :					int					):
									requires_backends(self       ,				['''transformers''', '''torch''', '''note_seq''']					)


				@classmethod
				def   A_ (		cls    :					List[Any]       ,				*lowercase_    :					Optional[Any]       ,				**lowercase_    :					str					):
									requires_backends(cls       ,				['''transformers''', '''torch''', '''note_seq''']					)


				@classmethod
				def   A_ (		cls    :					Tuple       ,				*lowercase_    :					Union[str, Any]       ,				**lowercase_    :					List[Any]					):
									requires_backends(cls       ,				['''transformers''', '''torch''', '''note_seq''']					)

