

'''simple docstring'''



# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue







def      a__ (						a__		):
     __SCREAMING_SNAKE_CASE						     =   Queue()
     __SCREAMING_SNAKE_CASE						     =   [False] * len(a__		)
     __SCREAMING_SNAKE_CASE						     =   [-1] * len(a__		)

     def bfs():
          while not queue.empty():
               __SCREAMING_SNAKE_CASE						     =   queue.get()
               __SCREAMING_SNAKE_CASE						     =   True

               for neighbour in graph[u]:
                    if neighbour == u:
                         return False

                    if color[neighbour] == -1:
                         __SCREAMING_SNAKE_CASE						     =   1 - color[u]
                         queue.put(a__		)

                    elif color[neighbour] == color[u]:
                         return False

          return True

     for i in range(len(a__		)		):
          if not visited[i]:
               queue.put(a__		)
               __SCREAMING_SNAKE_CASE						     =   0
               if bfs() is False:
                    return False

     return True


if __name__ == "__main__":
  # Adjacency List of graph
  print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))









'''simple docstring'''



from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxSeqaSeqConfigWithPast
from ...utils import logging


UpperCAmelCase				: Union[str, Any]         =  logging.get_logger(__name__)







class 		lowerCAmelCase__     (   a      ):



 """simple docstring"""



 lowerCAmelCase__						      =   "mt5"
 lowerCAmelCase__						      =   ["past_key_values"]
 def __init__(	self      : str      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=250_112      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=512      ,							__SCREAMING_SNAKE_CASE      : Optional[Any]=64      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=1_024      ,							__SCREAMING_SNAKE_CASE      : List[str]=8      ,							__SCREAMING_SNAKE_CASE      : Any=None      ,							__SCREAMING_SNAKE_CASE      : List[str]=6      ,							__SCREAMING_SNAKE_CASE      : Any=32      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=128      ,							__SCREAMING_SNAKE_CASE      : List[str]=0.1      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=1E-6      ,							__SCREAMING_SNAKE_CASE      : Optional[Any]=1.0      ,							__SCREAMING_SNAKE_CASE      : Tuple="gated-gelu"      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=True      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=True      ,							__SCREAMING_SNAKE_CASE      : Tuple="T5Tokenizer"      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=False      ,							__SCREAMING_SNAKE_CASE      : Tuple=0      ,							__SCREAMING_SNAKE_CASE      : str=1      ,							__SCREAMING_SNAKE_CASE      : Dict=0      ,							**__SCREAMING_SNAKE_CASE      : str      ,							)						->				List[Any]:


      """simple docstring"""




      super().__init__(
          is_encoder_decoder=__SCREAMING_SNAKE_CASE      ,							tokenizer_class=__SCREAMING_SNAKE_CASE      ,							tie_word_embeddings=__SCREAMING_SNAKE_CASE      ,							pad_token_id=__SCREAMING_SNAKE_CASE      ,							eos_token_id=__SCREAMING_SNAKE_CASE      ,							decoder_start_token_id=__SCREAMING_SNAKE_CASE      ,							**__SCREAMING_SNAKE_CASE      ,							)
      __SCREAMING_SNAKE_CASE						     =   vocab_size
      __SCREAMING_SNAKE_CASE						     =   d_model
      __SCREAMING_SNAKE_CASE						     =   d_kv
      __SCREAMING_SNAKE_CASE						     =   d_ff
      __SCREAMING_SNAKE_CASE						     =   num_layers
      __SCREAMING_SNAKE_CASE						     =   (
          num_decoder_layers if num_decoder_layers is not None else self.num_layers
      )  # default = symmetry
      __SCREAMING_SNAKE_CASE						     =   num_heads
      __SCREAMING_SNAKE_CASE						     =   relative_attention_num_buckets
      __SCREAMING_SNAKE_CASE						     =   relative_attention_max_distance
      __SCREAMING_SNAKE_CASE						     =   dropout_rate
      __SCREAMING_SNAKE_CASE						     =   layer_norm_epsilon
      __SCREAMING_SNAKE_CASE						     =   initializer_factor
      __SCREAMING_SNAKE_CASE						     =   feed_forward_proj
      __SCREAMING_SNAKE_CASE						     =   use_cache

      __SCREAMING_SNAKE_CASE						     =   self.feed_forward_proj.split("""-"""    )
      __SCREAMING_SNAKE_CASE						     =   act_info[-1]
      __SCREAMING_SNAKE_CASE						     =   act_info[0] == """gated"""

      if len(__SCREAMING_SNAKE_CASE    ) > 1 and act_info[0] != "gated" or len(__SCREAMING_SNAKE_CASE    ) > 2:
           raise ValueError(
               f'`feed_forward_proj`: {feed_forward_proj} is not a valid activation function of the dense layer.'
               """Please make sure `feed_forward_proj` is of the format `gated-{ACT_FN}` or `{ACT_FN}`, e.g. """
               """'gated-gelu' or 'relu'"""    )

      # for backwards compatibility
      if feed_forward_proj == "gated-gelu":
           __SCREAMING_SNAKE_CASE						     =   """gelu_new"""
 @property
 def    UpperCAmelCase__	(	self      : Optional[int]    )						->				str:


      """simple docstring"""




      return self.d_model
 @property
 def    UpperCAmelCase__	(	self      : List[str]    )						->				int:


      """simple docstring"""




      return self.num_heads


 @property
 def    UpperCAmelCase__	(	self      : List[str]    )						->				Union[str, Any]:


      """simple docstring"""




      return self.num_layers







class 		lowerCAmelCase__     (   a      ):



 """simple docstring"""



 @property
 # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
 def    UpperCAmelCase__	(	self      : Union[str, Any]    )						->				Mapping[str, Mapping[int, str]]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   {
          """input_ids""": {0: """batch""", 1: """encoder_sequence"""},
          """attention_mask""": {0: """batch""", 1: """encoder_sequence"""},
      }
      if self.use_past:
           __SCREAMING_SNAKE_CASE						     =   """past_encoder_sequence + sequence"""
           __SCREAMING_SNAKE_CASE						     =   {0: """batch"""}
           __SCREAMING_SNAKE_CASE						     =   {0: """batch""", 1: """past_decoder_sequence + sequence"""}
      else:
           __SCREAMING_SNAKE_CASE						     =   {0: """batch""", 1: """decoder_sequence"""}
           __SCREAMING_SNAKE_CASE						     =   {0: """batch""", 1: """decoder_sequence"""}

      if self.use_past:
           self.fill_with_past_key_values_(__SCREAMING_SNAKE_CASE      ,							direction="""inputs"""    )

      return common_inputs
 @property
 # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
 def    UpperCAmelCase__	(	self      : Optional[int]    )						->				int:


      """simple docstring"""




      return 13


 @property
 def    UpperCAmelCase__	(	self      : Tuple    )						->				float:


      """simple docstring"""




      return 5E-4






