


import heapq


def 				lowerCamelCase__	(      a	:   dict				)    ->	set[int]:





			"""simple docstring"""
			a__ :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(a	,  [-1 * len(a				), (key, value)]				)

			# chosen_vertices = set of chosen vertices
			a__ :List[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
						a__ :str						  =    heapq.heappop(a				)[1][0]
						chosen_vertices.add(a				)

						# 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]:
												a__ :List[str]						  =    elem[1][1].index(a				)
												del elem[1][1][index]
												elem[0] += 1
        # re-order the queue
						heapq.heapify(a				)
			return chosen_vertices


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		snake_case__			 =						{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)}''')






# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import argparse

from ...utils.dataclasses import (
    ComputeEnvironment,
    DistributedType,
    DynamoBackend,
    PrecisionType,
    SageMakerDistributedType,
)
from ..menu import BulletMenu


snake_case__			 =						[
    '''EAGER''',
    '''AOT_EAGER''',
    '''INDUCTOR''',
    '''NVFUSER''',
    '''AOT_NVFUSER''',
    '''AOT_CUDAGRAPHS''',
    '''OFI''',
    '''FX2TRT''',
    '''ONNXRT''',
    '''IPEX''',
]


def 				lowerCamelCase__	(      a	:   Optional[Any]	,  a	:   Tuple=None	,  a	:   int=None	,  a	:   List[str]=None				)    ->	int:





			"""simple docstring"""
			a__ :Tuple						  =    True
			while ask_again:
						a__ :str						  =    input(a				)
						try:
									if default is not None and len(a				) == 0:
												return default
									return convert_value(a				) if convert_value is not None else result
						except Exception:
									if error_message is not None:
												print(a				)


def 				lowerCamelCase__	(      a	:   int	,  a	:   Union[str, Any]=[]	,  a	:   str=None	,  a	:   str=0				)    ->	List[str]:





			"""simple docstring"""
			a__ :str						  =    BulletMenu(a	,  a				)
			a__ :int						  =    menu.run(default_choice=a				)
			return convert_value(a				) if convert_value is not None else result


def 				lowerCamelCase__	(      a	:   Optional[Any]				)    ->	Dict:





			"""simple docstring"""
			a__ :str						  =    int(a				)
			return ComputeEnvironment(["LOCAL_MACHINE", "AMAZON_SAGEMAKER"][value]				)


def 				lowerCamelCase__	(      a	:   Tuple				)    ->	List[str]:





			"""simple docstring"""
			a__ :Union[str, Any]						  =    int(a				)
			return DistributedType(["NO", "MULTI_CPU", "MULTI_XPU", "MULTI_GPU", "MULTI_NPU", "TPU"][value]				)


def 				lowerCamelCase__	(      a	:   List[Any]				)    ->	str:





			"""simple docstring"""
			a__ :int						  =    int(a				)
			return DynamoBackend(DYNAMO_BACKENDS[value]				).value


def 				lowerCamelCase__	(      a	:   Any				)    ->	Union[str, Any]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    int(a				)
			return PrecisionType(["no", "fp16", "bf16", "fp8"][value]				)


def 				lowerCamelCase__	(      a	:   List[Any]				)    ->	Union[str, Any]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    int(a				)
			return SageMakerDistributedType(["NO", "DATA_PARALLEL", "MODEL_PARALLEL"][value]				)


def 				lowerCamelCase__	(      a	:   Union[str, Any]				)    ->	List[str]:





			"""simple docstring"""
			return {"yes": True, "no": False}[value.lower()]







class 					lowerCAmelCase_ (       argparse.RawDescriptionHelpFormatter):




						def  _snake_case					(	self						:   Tuple   ,     __A						:   Tuple   ,     __A						:   int   ,     __A						:   Tuple   ,     __A						:   Any						)      ->Union[str, Any]:






									"""simple docstring"""






									a__ :Optional[int]						  =    super()._format_usage(__A   ,     __A   ,     __A   ,     __A						)
									a__ :Any						  =    usage.replace("<command> [<args>] "   ,     ""						)
									return usage


