



"""simple docstring"""





import heapq
def 	__lowerCAmelCase						(		__UpperCamelCase      :			dict    ):


						'''simple docstring'''






						snake_case_   : list[list]						=			[]

						# 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
						snake_case_   : Dict						=			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
												snake_case_   : str						=			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]:
																								snake_case_   : Dict						=			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       :					Tuple      					=					{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 math

import tensorflow as tf
from packaging import version
def 	__lowerCAmelCase						(		__UpperCamelCase      :			List[Any]    ):


						'''simple docstring'''






						snake_case_   : int						=			tf.convert_to_tensor(__UpperCamelCase    )
						snake_case_   : int						=			0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0    )					, x.dtype    )    ))

						return x * cdf
def 	__lowerCAmelCase						(		__UpperCamelCase      :			List[str]    ):


						'''simple docstring'''






						snake_case_   : int						=			tf.convert_to_tensor(__UpperCamelCase    )
						snake_case_   : List[Any]						=			tf.cast(math.pi					, x.dtype    )
						snake_case_   : int						=			tf.cast(0.044_715					, x.dtype    )
						snake_case_   : Optional[int]						=			0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi    ) * (x + coeff * tf.pow(__UpperCamelCase					, 3    ))    ))

						return x * cdf
def 	__lowerCAmelCase						(		__UpperCamelCase      :			str    ):


						'''simple docstring'''






						snake_case_   : Optional[Any]						=			tf.convert_to_tensor(__UpperCamelCase    )

						return x * tf.tanh(tf.math.softplus(__UpperCamelCase    )    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any    ):


						'''simple docstring'''






						snake_case_   : str						=			tf.convert_to_tensor(__UpperCamelCase    )
						snake_case_   : int						=			tf.cast(0.044_715					, x.dtype    )
						snake_case_   : Optional[int]						=			tf.cast(0.7_978_845_608					, x.dtype    )

						return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x)    ))
def 	__lowerCAmelCase						(		__UpperCamelCase      :			List[str]    ):


						'''simple docstring'''






						snake_case_   : Tuple						=			tf.convert_to_tensor(__UpperCamelCase    )
						snake_case_   : str						=			tf.cast(1.702					, x.dtype    )
						return x * tf.math.sigmoid(coeff * x    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			int    ):


						'''simple docstring'''






						return tf.clip_by_value(_gelu(__UpperCamelCase    )					, -1_0					, 1_0    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Optional[int]					, __UpperCamelCase      :			List[str]=-1    ):


						'''simple docstring'''






						snake_case_			,		snake_case_   : List[Any]						=			tf.split(__UpperCamelCase					, 2					, axis=__UpperCamelCase    )
						return a * tf.math.sigmoid(__UpperCamelCase    )


if version.parse(tf.version.VERSION) >= version.parse('''2.4'''):
					def 	__lowerCAmelCase						(		__UpperCamelCase      :			List[Any]    ):


											'''simple docstring'''






											return tf.keras.activations.gelu(__UpperCamelCase					, approximate=__UpperCamelCase    )

					__lowerCAmelCase       :					int      					=					tf.keras.activations.gelu






					__lowerCAmelCase       :					Optional[Any]      					=					approximate_gelu_wrap
else:
					__lowerCAmelCase       :					List[Any]      					=					_gelu
					__lowerCAmelCase       :					Any      					=					_gelu_new


__lowerCAmelCase       :					Dict      					=					{
    '''gelu''': gelu,
    '''gelu_10''': gelu_aa,
    '''gelu_fast''': gelu_fast,
    '''gelu_new''': gelu_new,
    '''glu''': glu,
    '''mish''': mish,
    '''quick_gelu''': quick_gelu,
    '''relu''': tf.keras.activations.relu,
    '''sigmoid''': tf.keras.activations.sigmoid,
    '''silu''': tf.keras.activations.swish,
    '''swish''': tf.keras.activations.swish,
    '''tanh''': tf.keras.activations.tanh,
}






def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any    ):


						'''simple docstring'''






						if activation_string in ACTaFN:
												return ACTaFN[activation_string]
						else:
												raise KeyError(F'function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys()    )}'    )

