





'''simple docstring'''






import heapq






def      __A						(							a_						:  dict	):
		lowerCAmelCase     :    List[str]						=   []

		# for each node and his adjacency list add them and the rank of the node to queue
		# using heapq module the queue will be filled like a Priority Queue
		# heapq works with a min priority queue, so I used -1*len(v) to build it
		for key, value in graph.items():
				# O(log(n))
				heapq.heappush(_UpperCamelCase      ,[-1 * len(_UpperCamelCase	), (key, value)]	)

		# chosen_vertices = set of chosen vertices
		lowerCAmelCase     :    Optional[Any]						=   set()

		# while queue isn't empty and there are still edges
		#   (queue[0][0] is the rank of the node with max rank)
		while queue and queue[0][0] != 0:
				# extract vertex with max rank from queue and add it to chosen_vertices
				lowerCAmelCase     :    Optional[Any]						=   heapq.heappop(_UpperCamelCase	)[1][0]
				chosen_vertices.add(_UpperCamelCase	)

				# Remove all arcs adjacent to argmax
				for elem in queue:
						# if v haven't adjacent node, skip
						if elem[0] == 0:
								continue
						# if argmax is reachable from elem
						# remove argmax from elem's adjacent list and update his rank
						if argmax in elem[1][1]:
								lowerCAmelCase     :    Any						=   elem[1][1].index(_UpperCamelCase	)
								del elem[1][1][index]
								elem[0] += 1
        # re-order the queue
				heapq.heapify(_UpperCamelCase	)
		return chosen_vertices


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			lowerCAmelCase       		=      {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
			print(F'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')










'''simple docstring'''






import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import TaBlock, TaConfig, TaLayerNorm

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin
class 		lowerCamelCase  (      _A      ,   _A      ,   _A       ):



	@register_to_config
	def __init__(   self		,      a_		,      a_		,      a_		,      a_		,      a_		,      a_		,      a_		,      a_		,      a_		,      a_ = False		,      ):
			super().__init__()

			lowerCAmelCase     :    int						=   nn.Embedding(a_		,      a_	)

			lowerCAmelCase     :    int						=   nn.Embedding(a_		,      a_	)
			lowerCAmelCase     :    int						=   False

			lowerCAmelCase     :    int						=   nn.Dropout(p=a_	)

			lowerCAmelCase     :    str						=   TaConfig(
			    vocab_size=a_		,      d_model=a_		,      num_heads=a_		,      d_kv=a_		,      d_ff=a_		,      dropout_rate=a_		,      feed_forward_proj=a_		,      is_decoder=a_		,      is_encoder_decoder=a_		,      )

			lowerCAmelCase     :    Any						=   nn.ModuleList()
			for lyr_num in range(a_	):
					lowerCAmelCase     :    Optional[Any]						=   TaBlock(a_	)
					self.encoders.append(a_	)

			lowerCAmelCase     :    List[str]						=   TaLayerNorm(a_	)
			lowerCAmelCase     :    Union[str, Any]						=   nn.Dropout(p=a_	)





	def   _lowerCamelCase    (   self		,      a_		,      a_	):
			lowerCAmelCase     :    Optional[Any]						=   self.token_embedder(a_	)

			lowerCAmelCase     :    int						=   encoder_input_tokens.shape[1]
			lowerCAmelCase     :    Optional[int]						=   torch.arange(a_		,      device=encoder_input_tokens.device	)
			x += self.position_encoding(a_	)

			lowerCAmelCase     :    List[str]						=   self.dropout_pre(a_	)

			# inverted the attention mask
			lowerCAmelCase     :    List[Any]						=   encoder_input_tokens.size()
			lowerCAmelCase     :    Dict						=   self.get_extended_attention_mask(a_		,      a_	)

			for lyr in self.encoders:
					lowerCAmelCase     :    Dict						=   lyr(a_		,      a_	)[0]
			lowerCAmelCase     :    int						=   self.layer_norm(a_	)

			return self.dropout_post(a_	), encoder_inputs_mask



