


"""simple docstring"""







# using dfs for finding eulerian path traversal




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_=None   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				(path or []) + [u]
					for v in graph[u]:
										if visited_edge[u][v] is False:
															__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				True, True
															__SCREAMING_SNAKE_CASE						   =				dfs(lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )
					return path




def    UpperCAmelCase__       (lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				0
					__SCREAMING_SNAKE_CASE						   =				-1
					for i in range(lowerCAmelCase_   ):
										if i not in graph.keys():
															continue
										if len(graph[i]   ) % 2 == 1:
															odd_degree_nodes += 1
															__SCREAMING_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__       (lowerCAmelCase_  ,						lowerCAmelCase_   ):




					'''simple docstring'''


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




def    UpperCAmelCase__       ():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
					__SCREAMING_SNAKE_CASE						   =				{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
					__SCREAMING_SNAKE_CASE						   =				{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
					__SCREAMING_SNAKE_CASE						   =				{1: [2, 3], 2: [1, 3], 3: [1, 2]}
					__SCREAMING_SNAKE_CASE						   =				{
					    1: [],
					    2: []
					    # all degree is zero
					}
					__SCREAMING_SNAKE_CASE						   =				10
					check_euler(lowerCAmelCase_  ,						lowerCAmelCase_   )
					check_euler(lowerCAmelCase_  ,						lowerCAmelCase_   )
					check_euler(lowerCAmelCase_  ,						lowerCAmelCase_   )
					check_euler(lowerCAmelCase_  ,						lowerCAmelCase_   )
					check_euler(lowerCAmelCase_  ,						lowerCAmelCase_   )


if __name__ == "__main__":
		main()


"""simple docstring"""





from ..utils import DummyObject, requires_backends
class 						SCREAMING_SNAKE_CASE_ (						metaclass=__a ):




		"""simple docstring"""





		__lowercase							:  Tuple						   =		['''keras_nlp''']




		def __init__(     self							,  *lowerCAmelCase__							,  **lowerCAmelCase__):
				requires_backends(self							,  ["""keras_nlp"""])




