





def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_		,lowercase_=None			)					->		Union[str, Any]:




      """simple docstring"""

      _UpperCamelCase      :	Tuple						=       (path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  _UpperCamelCase      :	Any						=       True, True
                  _UpperCamelCase      :	Optional[int]						=       dfs(lowercase_		,lowercase_		,lowercase_		,lowercase_			)
      return path




def 					lowercase__    (					lowercase_		,lowercase_			)					->		Any:




      """simple docstring"""

      _UpperCamelCase      :	Tuple						=       0
      _UpperCamelCase      :	Tuple						=       -1
      for i in range(lowercase_			):
            if i not in graph.keys():
                  continue
            if len(graph[i]			) % 2 == 1:
                  odd_degree_nodes += 1
                  _UpperCamelCase      :	str						=       i
      if odd_degree_nodes == 0:
            return 1, odd_node
      if odd_degree_nodes == 2:
            return 2, odd_node
      return 3, odd_node




def 					lowercase__    (					lowercase_		,lowercase_			)					->		Dict:




      """simple docstring"""

      _UpperCamelCase      :	List[str]						=       [[False for _ in range(max_node + 1			)] for _ in range(max_node + 1			)]
      _UpperCamelCase      :	Any						=       check_circuit_or_path(lowercase_		,lowercase_			)
      if check == 3:
            print("graph is not Eulerian"			)
            print("no path"			)
            return
      _UpperCamelCase      :	int						=       1
      if check == 2:
            _UpperCamelCase      :	Optional[Any]						=       odd_node
            print("graph has a Euler path"			)
      if check == 1:
            print("graph has a Euler cycle"			)
      _UpperCamelCase      :	Any						=       dfs(lowercase_		,lowercase_		,lowercase_			)
      print(lowercase_			)




def 					lowercase__    (					)					->		Dict:




      """simple docstring"""

      _UpperCamelCase      :	Union[str, Any]						=       {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      _UpperCamelCase      :	Any						=       {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      _UpperCamelCase      :	List[Any]						=       {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      _UpperCamelCase      :	Optional[int]						=       {1: [2, 3], 2: [1, 3], 3: [1, 2]}
      _UpperCamelCase      :	Tuple						=       {
          1: [],
          2: []
          # all degree is zero
      }
      _UpperCamelCase      :	Optional[int]						=       10
      check_euler(lowercase_		,lowercase_			)
      check_euler(lowercase_		,lowercase_			)
      check_euler(lowercase_		,lowercase_			)
      check_euler(lowercase_		,lowercase_			)
      check_euler(lowercase_		,lowercase_			)


if __name__ == "__main__":
  main()







"""simple docstring"""


def 					lowercase__    (					lowercase_		,lowercase_			)					->		None:




      """simple docstring"""

      _UpperCamelCase      :	List[Any]						=       len(lowercase_			)
      print("The following activities are selected:"			)

      # The first activity is always selected
      _UpperCamelCase      :	List[Any]						=       0
      print(lowercase_		,end=","			)

      # Consider rest of the activities
      for j in range(lowercase_			):
            # If this activity has start time greater than
            # or equal to the finish time of previously
            # selected activity, then select it
            if start[j] >= finish[i]:
                  print(lowercase_		,end=","			)
                  _UpperCamelCase      :	Optional[Any]						=       j


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  lowerCamelCase__				  =   [1, 3, 0, 5, 8, 5]
  lowerCamelCase__				  =   [2, 4, 6, 7, 9, 9]
  print_max_activities(start, finish)
