
'''simple docstring'''






# using dfs for finding eulerian path traversal







def 		A_							(						_lowerCAmelCase :     str					,						_lowerCAmelCase :     Union[str, Any]					,						_lowerCAmelCase :     Optional[Any]					,						_lowerCAmelCase :     Union[str, Any]=None				):



      """simple docstring"""




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







def 		A_							(						_lowerCAmelCase :     Dict					,						_lowerCAmelCase :     List[str]				):



      """simple docstring"""




      _lowerCamelCase					: Tuple		    = 0
      _lowerCamelCase					: List[Any]		    = -1
      for i in range(_lowerCAmelCase				):
            if i not in graph.keys():
                  continue
            if len(graph[i]				) % 2 == 1:
                  odd_degree_nodes += 1
                  _lowerCamelCase					: Dict		    = i
      if odd_degree_nodes == 0:
            return 1, odd_node
      if odd_degree_nodes == 2:
            return 2, odd_node
      return 3, odd_node







def 		A_							(						_lowerCAmelCase :     List[Any]					,						_lowerCAmelCase :     Dict				):



      """simple docstring"""




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







def 		A_							(						):



      """simple docstring"""




      _lowerCamelCase					: Optional[Any]		    = {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      _lowerCamelCase					: Union[str, Any]		    = {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      _lowerCamelCase					: Tuple		    = {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      _lowerCamelCase					: Dict		    = {1: [2, 3], 2: [1, 3], 3: [1, 2]}
      _lowerCamelCase					: List[Any]		    = {
          1: [],
          2: []
          # all degree is zero
      }
      _lowerCamelCase					: Optional[Any]		    = 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 dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Features, Value
from .base import TaskTemplate





@dataclass(frozen=SCREAMING_SNAKE_CASE    )
class lowerCamelCase__   (				SCREAMING_SNAKE_CASE    ):



    '''simple docstring'''




    _lowerCamelCase					=   field(default='''summarization'''     ,   metadata={'''include_in_asdict_even_if_is_default''': True}    )
    _lowerCamelCase					=   Features({'''text''': Value('''string'''    )}    )
    _lowerCamelCase					=   Features({'''summary''': Value('''string'''    )}    )
    _lowerCamelCase					=   "text"
    _lowerCamelCase					=   "summary"




    @property
    def UpperCamelCase__		( self    )    ->      Dict[str, str]:
          return {self.text_column: "text", self.summary_column: "summary"}




