


'''simple docstring'''

# using dfs for finding eulerian path traversal






def __UpperCamelCase   (			__lowerCamelCase		: int      ,  __lowerCamelCase		: str      ,  __lowerCamelCase		: Union[str, Any]      ,  __lowerCamelCase		: Dict=None				)      ->     Optional[Any]:







     '''simple docstring'''






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






def __UpperCamelCase   (			__lowerCamelCase		: List[str]      ,  __lowerCamelCase		: Optional[Any]				)      ->     Tuple:







     '''simple docstring'''






     _a						=		0
     _a						=		-1
     for i in range(__lowerCamelCase				):
          if i not in graph.keys():
               continue
          if len(graph[i]				) % 2 == 1:
               odd_degree_nodes += 1
               _a						=		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		: str      ,  __lowerCamelCase		: Any				)      ->     List[Any]:







     '''simple docstring'''






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






def __UpperCamelCase   (			)      ->     Optional[int]:







     '''simple docstring'''






     _a						=		{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
     _a						=		{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
     _a						=		{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
     _a						=		{1: [2, 3], 2: [1, 3], 3: [1, 2]}
     _a						=		{
         1: [],
         2: []
         # all degree is zero
     }
     _a						=		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 typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase__				     =		{
    "configuration_mctct": ["MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP", "MCTCTConfig"],
    "feature_extraction_mctct": ["MCTCTFeatureExtractor"],
    "processing_mctct": ["MCTCTProcessor"],
}


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowercase__				     =		[
       "MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST",
       "MCTCTForCTC",
       "MCTCTModel",
       "MCTCTPreTrainedModel",
   ]


if TYPE_CHECKING:
   from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
   from .feature_extraction_mctct import MCTCTFeatureExtractor
   from .processing_mctct import MCTCTProcessor

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
   import sys

   lowercase__				     =		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

