

'''simple docstring'''
# using dfs for finding eulerian path traversal




def 	UpperCamelCase   (       lowercase_						:    Any     ,					lowercase_						:    List[str]     ,					lowercase_						:    List[Any]     ,					lowercase_						:    Union[str, Any]=None	)		->	Dict:




  '''simple docstring'''



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




def 	UpperCamelCase   (       lowercase_						:    List[Any]     ,					lowercase_						:    Union[str, Any]	)		->	Optional[Any]:




  '''simple docstring'''



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




  '''simple docstring'''



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




def 	UpperCamelCase   (       )		->	List[Any]:




  '''simple docstring'''



  lowercase									={1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
  lowercase									={1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
  lowercase									={1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
  lowercase									={1: [2, 3], 2: [1, 3], 3: [1, 2]}
  lowercase									={
      1: [],
      2: []
      # all degree is zero
  }
  lowercase									=1_0
  check_euler(lowercase_     ,					lowercase_	)
  check_euler(lowercase_     ,					lowercase_	)
  check_euler(lowercase_     ,					lowercase_	)
  check_euler(lowercase_     ,					lowercase_	)
  check_euler(lowercase_     ,					lowercase_	)


if __name__ == "__main__":
     main()







from typing import TYPE_CHECKING

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


A       :   Optional[int]					= {
    '''configuration_pix2struct''': [
        '''PIX2STRUCT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''Pix2StructConfig''',
        '''Pix2StructTextConfig''',
        '''Pix2StructVisionConfig''',
    ],
    '''processing_pix2struct''': ['''Pix2StructProcessor'''],
}

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					A       :   Optional[int]					= ['''Pix2StructImageProcessor''']


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					A       :   Dict					= [
					    '''PIX2STRUCT_PRETRAINED_MODEL_ARCHIVE_LIST''',
					    '''Pix2StructPreTrainedModel''',
					    '''Pix2StructForConditionalGeneration''',
					    '''Pix2StructVisionModel''',
					    '''Pix2StructTextModel''',
					]

if TYPE_CHECKING:
					from .configuration_pixastruct import (
					    PIX2STRUCT_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    PixaStructConfig,
					    PixaStructTextConfig,
					    PixaStructVisionConfig,
					)
					from .processing_pixastruct import PixaStructProcessor

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .image_processing_pixastruct import PixaStructImageProcessor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_pixastruct import (
										    PIX2STRUCT_PRETRAINED_MODEL_ARCHIVE_LIST,
										    PixaStructForConditionalGeneration,
										    PixaStructPreTrainedModel,
										    PixaStructTextModel,
										    PixaStructVisionModel,
										)

else:
					import sys

					A       :   Any					= _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



