





'''simple docstring'''







# using dfs for finding eulerian path traversal

def    __UpperCamelCase	(	a    : Tuple					,   a    : str					,   a    : Any					,   a    : int=None     ) ->Any:
 snake_case				=			(path or []) + [u]
 for v in graph[u]:
  if visited_edge[u][v] is False:
   snake_case				,		snake_case				=			True, True
   snake_case				=			dfs(a					,   a					,   a					,   a     )
 return path

def    __UpperCamelCase	(	a    : Optional[int]					,   a    : Optional[int]     ) ->List[Any]:
 snake_case				=			0
 snake_case				=			-1
 for i in range(a     ):
  if i not in graph.keys():
   continue
  if len(graph[i]     ) % 2 == 1:
   odd_degree_nodes += 1
   snake_case				=			i
 if odd_degree_nodes == 0:
  return 1, odd_node
 if odd_degree_nodes == 2:
  return 2, odd_node
 return 3, odd_node

def    __UpperCamelCase	(	a    : Dict					,   a    : Any     ) ->Dict:
 snake_case				=			[[False for _ in range(max_node + 1     )] for _ in range(max_node + 1     )]
 snake_case				,		snake_case				=			check_circuit_or_path(a					,   a     )
 if check == 3:
  print('''graph is not Eulerian'''     )
  print('''no path'''     )
  return
 snake_case				=			1
 if check == 2:
  snake_case				=			odd_node
  print('''graph has a Euler path'''     )
 if check == 1:
  print('''graph has a Euler cycle'''     )
 snake_case				=			dfs(a					,   a					,   a     )
 print(a     )

def    __UpperCamelCase	(	) ->Tuple:
 snake_case				=			{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
 snake_case				=			{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
 snake_case				=			{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
 snake_case				=			{1: [2, 3], 2: [1, 3], 3: [1, 2]}
 snake_case				=			{
     1: [],
     2: []
     # all degree is zero
 }
 snake_case				=			10
 check_euler(a					,   a     )
 check_euler(a					,   a     )
 check_euler(a					,   a     )
 check_euler(a					,   a     )
 check_euler(a					,   a     )


if __name__ == "__main__":
   main()








'''simple docstring'''







from ..utils import DummyObject, requires_backends
class 			_lowercase						(       metaclass=__a					):
     _UpperCAmelCase										=					['''transformers''', '''torch''', '''note_seq''']







     def __init__( self    ,   *A__    ,   **A__    ) ->	Union[str, Any]:
      requires_backends(self    ,   ['''transformers''', '''torch''', '''note_seq''']    )







     @classmethod
     def     UpperCamelCase			( cls    ,   *A__    ,   **A__    ) ->	Optional[Any]:
      requires_backends(cls    ,   ['''transformers''', '''torch''', '''note_seq''']    )







     @classmethod
     def     UpperCamelCase			( cls    ,   *A__    ,   **A__    ) ->	Any:
      requires_backends(cls    ,   ['''transformers''', '''torch''', '''note_seq''']    )

