




# using dfs for finding eulerian path traversal








def 						SCREAMING_SNAKE_CASE       (      a_	:							Any				,					a_	:							Union[str, Any]				,					a_	:							Union[str, Any]				,					a_	:							Tuple=None			):
  __a			=					(path or []) + [u]
  for v in graph[u]:
    if visited_edge[u][v] is False:
      __a	,       __a			=					True, True
      __a			=					dfs(snake_case__				,					snake_case__				,					snake_case__				,					snake_case__			)
  return path


def 						SCREAMING_SNAKE_CASE       (      a_	:							List[Any]				,					a_	:							str			):
  __a			=					0
  __a			=					-1
  for i in range(snake_case__			):
    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 						SCREAMING_SNAKE_CASE       (      a_	:							Union[str, Any]				,					a_	:							Any			):
  __a			=					[[False for _ in range(max_node + 1			)] for _ in range(max_node + 1			)]
  __a	,       __a			=					check_circuit_or_path(snake_case__				,					snake_case__			)
  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(snake_case__				,					snake_case__				,					snake_case__			)
  print(snake_case__			)


def 						SCREAMING_SNAKE_CASE       (      ):
  __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(snake_case__				,					snake_case__			)
  check_euler(snake_case__				,					snake_case__			)
  check_euler(snake_case__				,					snake_case__			)
  check_euler(snake_case__				,					snake_case__			)
  check_euler(snake_case__				,					snake_case__			)


if __name__ == "__main__":
  main()









'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase_ 		=      {
    "configuration_roformer": ["ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "RoFormerConfig", "RoFormerOnnxConfig"],
    "tokenization_roformer": ["RoFormerTokenizer"],
}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_ 		=      ["RoFormerTokenizerFast"]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_ 		=      [
      "ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
      "RoFormerForCausalLM",
      "RoFormerForMaskedLM",
      "RoFormerForMultipleChoice",
      "RoFormerForQuestionAnswering",
      "RoFormerForSequenceClassification",
      "RoFormerForTokenClassification",
      "RoFormerLayer",
      "RoFormerModel",
      "RoFormerPreTrainedModel",
      "load_tf_weights_in_roformer",
  ]


try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_ 		=      [
      "TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
      "TFRoFormerForCausalLM",
      "TFRoFormerForMaskedLM",
      "TFRoFormerForMultipleChoice",
      "TFRoFormerForQuestionAnswering",
      "TFRoFormerForSequenceClassification",
      "TFRoFormerForTokenClassification",
      "TFRoFormerLayer",
      "TFRoFormerModel",
      "TFRoFormerPreTrainedModel",
  ]


try:
  if not is_flax_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_ 		=      [
      "FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
      "FlaxRoFormerForMaskedLM",
      "FlaxRoFormerForMultipleChoice",
      "FlaxRoFormerForQuestionAnswering",
      "FlaxRoFormerForSequenceClassification",
      "FlaxRoFormerForTokenClassification",
      "FlaxRoFormerModel",
      "FlaxRoFormerPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_roformer import ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, RoFormerConfig, RoFormerOnnxConfig
  from .tokenization_roformer import RoFormerTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_roformer_fast import RoFormerTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_roformer import (
        ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
        RoFormerForCausalLM,
        RoFormerForMaskedLM,
        RoFormerForMultipleChoice,
        RoFormerForQuestionAnswering,
        RoFormerForSequenceClassification,
        RoFormerForTokenClassification,
        RoFormerLayer,
        RoFormerModel,
        RoFormerPreTrainedModel,
        load_tf_weights_in_roformer,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_roformer import (
        TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFRoFormerForCausalLM,
        TFRoFormerForMaskedLM,
        TFRoFormerForMultipleChoice,
        TFRoFormerForQuestionAnswering,
        TFRoFormerForSequenceClassification,
        TFRoFormerForTokenClassification,
        TFRoFormerLayer,
        TFRoFormerModel,
        TFRoFormerPreTrainedModel,
    )

  try:
    if not is_flax_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flax_roformer import (
        FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
        FlaxRoFormerForMaskedLM,
        FlaxRoFormerForMultipleChoice,
        FlaxRoFormerForQuestionAnswering,
        FlaxRoFormerForSequenceClassification,
        FlaxRoFormerForTokenClassification,
        FlaxRoFormerModel,
        FlaxRoFormerPreTrainedModel,
    )


else:
  import sys

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



