






import heapq







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							dict     ):
	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(snake_case_  ,						[-1 * len(snake_case_     ), (key, value)]     )

	# chosen_vertices = set of chosen vertices
	snake_case__				:   Tuple     =						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__				:   List[Any]     =						heapq.heappop(snake_case_     )[1][0]
		chosen_vertices.add(snake_case_     )

		# 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__				:   Tuple     =						elem[1][1].index(snake_case_     )
				del elem[1][1][index]
				elem[0] += 1
        # re-order the queue
		heapq.heapify(snake_case_     )
	return chosen_vertices


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	__lowerCamelCase      :    Dict   		=   {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)}")











# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING, Dict, Optional

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.logging import get_logger
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
	import jax
	import jaxlib

__lowerCamelCase      :    Optional[int]   		=   get_logger()

__lowerCamelCase      :    Optional[dict]   		=   None



class 							SCREAMING_SNAKE_CASE__		(       TensorFormatter[Mapping, "jax.Array", Mapping]		):





					"""simple docstring"""






					def __init__(      self  :						Optional[Any]							,	__A  :						Dict=None							,	__A  :						List[str]=None							,	**__A  :						str ):
						super().__init__(features=__A )
						import jax
						from jaxlib.xla_client import Device

						if isinstance(__A							,	__A ):
							raise ValueError(
							    f'''Expected {device} to be a `str` not {type(__A )}, as `jaxlib.xla_extension.Device` '''
							    "is not serializable neither with `pickle` nor with `dill`. Instead you can surround "
							    "the device with `str()` to get its string identifier that will be internally mapped "
							    "to the actual `jaxlib.xla_extension.Device`." )
						snake_case__				:   List[Any]     =						device if isinstance(__A							,	__A ) else str(jax.devices()[0] )
						# using global variable since `jaxlib.xla_extension.Device` is not serializable neither
						# with `pickle` nor with `dill`, so we need to use a global variable instead
						global DEVICE_MAPPING
						if DEVICE_MAPPING is None:
							snake_case__				:   Any     =						self._map_devices_to_str()
						if self.device not in list(DEVICE_MAPPING.keys() ):
							logger.warning(
							    f'''Device with string identifier {self.device} not listed among the available '''
							    f'''devices: {list(DEVICE_MAPPING.keys() )}, so falling back to the default '''
							    f'''device: {str(jax.devices()[0] )}.''' )
							snake_case__				:   str     =						str(jax.devices()[0] )
						snake_case__				:   str     =						jnp_array_kwargs



					@staticmethod
					def  _lowercase  (      ):
						import jax

						return {str(__A ): device for device in jax.devices()}



					def  _lowercase  (      self  :						Optional[Any]							,	__A  :						str ):
						import jax
						import jax.numpy as jnp

						if isinstance(__A							,	__A ) and column:
							if all(
							    isinstance(__A							,	jax.Array ) and x.shape == column[0].shape and x.dtype == column[0].dtype for x in column ):
								return jnp.stack(__A							,	axis=0 )
						return column



					def  _lowercase  (      self  :						int							,	__A  :						Tuple ):
						import jax
						import jax.numpy as jnp

						if isinstance(__A							,	(str, bytes, type(__A )) ):
							return value
						elif isinstance(__A							,	(np.character, np.ndarray) ) and np.issubdtype(value.dtype							,	np.character ):
							return value.tolist()

						snake_case__				:   Optional[int]     =						{}

						if isinstance(__A							,	(np.number, np.ndarray) ) and np.issubdtype(value.dtype							,	np.integer ):
							# the default int precision depends on the jax config
							# see https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#double-64bit-precision
							if jax.config.jax_enable_xaa:
								snake_case__				:   Any     =						{"dtype": jnp.intaa}
							else:
								snake_case__				:   Tuple     =						{"dtype": jnp.intaa}
						elif isinstance(__A							,	(np.number, np.ndarray) ) and np.issubdtype(value.dtype							,	np.floating ):
							snake_case__				:   str     =						{"dtype": jnp.floataa}
						elif config.PIL_AVAILABLE and "PIL" in sys.modules:
							import PIL.Image

							if isinstance(__A							,	PIL.Image.Image ):
								snake_case__				:   Optional[Any]     =						np.asarray(__A )

        # using global variable since `jaxlib.xla_extension.Device` is not serializable neither
        # with `pickle` nor with `dill`, so we need to use a global variable instead
						global DEVICE_MAPPING
						if DEVICE_MAPPING is None:
							snake_case__				:   int     =						self._map_devices_to_str()

						with jax.default_device(DEVICE_MAPPING[self.device] ):
							# calling jnp.array on a np.ndarray does copy the data
							# see https://github.com/google/jax/issues/4486
							return jnp.array(__A							,	**{**default_dtype, **self.jnp_array_kwargs} )



					def  _lowercase  (      self  :						Union[str, Any]							,	__A  :						Optional[int] ):
						import jax

						# support for torch, tf, jax etc.
						if config.TORCH_AVAILABLE and "torch" in sys.modules:
							import torch

							if isinstance(__A							,	torch.Tensor ):
								return self._tensorize(data_struct.detach().cpu().numpy()[()] )
						if hasattr(__A							,	"__array__" ) and not isinstance(__A							,	jax.Array ):
							snake_case__				:   Union[str, Any]     =						data_struct.__array__()
						# support for nested types like struct of list of struct
						if isinstance(__A							,	np.ndarray ):
							if data_struct.dtype == object:  # jax arrays cannot be instantied from an array of objects
								return self._consolidate([self.recursive_tensorize(__A ) for substruct in data_struct] )
						elif isinstance(__A							,	(list, tuple) ):
							return self._consolidate([self.recursive_tensorize(__A ) for substruct in data_struct] )
						return self._tensorize(__A )



					def  _lowercase  (      self  :						Tuple							,	__A  :						dict ):
						return map_nested(self._recursive_tensorize							,	__A							,	map_list=__A )



					def  _lowercase  (      self  :						Optional[int]							,	__A  :						pa.Table ):
						snake_case__				:   int     =						self.numpy_arrow_extractor().extract_row(__A )
						snake_case__				:   Tuple     =						self.python_features_decoder.decode_row(__A )
						return self.recursive_tensorize(__A )



					def  _lowercase  (      self  :						Optional[Any]							,	__A  :						pa.Table ):
						snake_case__				:   Any     =						self.numpy_arrow_extractor().extract_column(__A )
						snake_case__				:   Optional[int]     =						self.python_features_decoder.decode_column(__A							,	pa_table.column_names[0] )
						snake_case__				:   List[Any]     =						self.recursive_tensorize(__A )
						snake_case__				:   Dict     =						self._consolidate(__A )
						return column






					def  _lowercase  (      self  :						str							,	__A  :						pa.Table ):
						snake_case__				:   Any     =						self.numpy_arrow_extractor().extract_batch(__A )
						snake_case__				:   int     =						self.python_features_decoder.decode_batch(__A )
						snake_case__				:   List[Any]     =						self.recursive_tensorize(__A )
						for column_name in batch:
							snake_case__				:   Any     =						self._consolidate(batch[column_name] )
						return batch



