




def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )			->							List[str]:


			'''simple docstring'''







			global f  # a global dp table for knapsack
			if f[i][j] < 0:
						if j < wt[i - 1]:
									SCREAMING_SNAKE_CASE_								=						mf_knapsack(i - 1       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )
						else:
									SCREAMING_SNAKE_CASE_								=						max(
									    mf_knapsack(i - 1       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )       ,    mf_knapsack(i - 1       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    j - wt[i - 1] ) + val[i - 1]       ,    )
						SCREAMING_SNAKE_CASE_								=						val
			return f[i][j]

def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )			->							Tuple:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						[[0] * (w + 1) for _ in range(n + 1 )]

			for i in range(1       ,    n + 1 ):
						for w_ in range(1       ,    w + 1 ):
									if wt[i - 1] <= w_:
												SCREAMING_SNAKE_CASE_								=						max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]       ,    dp[i - 1][w_] )
									else:
												SCREAMING_SNAKE_CASE_								=						dp[i - 1][w_]

			return dp[n][w_], dp

def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )			->							List[Any]:


			'''simple docstring'''







			if not (isinstance(SCREAMING_SNAKE_CASE       ,    (list, tuple) ) and isinstance(SCREAMING_SNAKE_CASE       ,    (list, tuple) )):
						raise ValueError(
						    'Both the weights and values vectors must be either lists or tuples' )

			SCREAMING_SNAKE_CASE_								=						len(SCREAMING_SNAKE_CASE )
			if num_items != len(SCREAMING_SNAKE_CASE ):
						SCREAMING_SNAKE_CASE_								=						(
						    'The number of weights must be the same as the number of values.\n'
						    F'But got {num_items} weights and {len(SCREAMING_SNAKE_CASE )} values'
						)
						raise ValueError(SCREAMING_SNAKE_CASE )
			for i in range(SCREAMING_SNAKE_CASE ):
						if not isinstance(wt[i]       ,    SCREAMING_SNAKE_CASE ):
									SCREAMING_SNAKE_CASE_								=						(
									    'All weights must be integers but got weight of '
									    F'type {type(wt[i] )} at index {i}'
									)
									raise TypeError(SCREAMING_SNAKE_CASE )

			SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						knapsack(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )
			SCREAMING_SNAKE_CASE_								=						set()
			_construct_solution(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )

			return optimal_val, example_optional_set

def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )			->							Union[str, Any]:


			'''simple docstring'''







			if i > 0 and j > 0:
						if dp[i - 1][j] == dp[i][j]:
									_construct_solution(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    i - 1       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )
						else:
									optimal_set.add(SCREAMING_SNAKE_CASE )
									_construct_solution(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    i - 1       ,    j - wt[i - 1]       ,    SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
				SCREAMING_SNAKE_CASE__     :     Optional[Any]		    =       [3, 2, 4, 4]
				SCREAMING_SNAKE_CASE__     :     List[str]		    =       [4, 3, 2, 3]
				SCREAMING_SNAKE_CASE__     :     Optional[Any]		    =       4
				SCREAMING_SNAKE_CASE__     :     Any		    =       6
				SCREAMING_SNAKE_CASE__     :     Union[str, Any]		    =       [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
				SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__     :     Optional[Any]		    =       knapsack(w, wt, val, n)
				print(optimal_solution)
				print(mf_knapsack(n, wt, val, w))  # switched the n and w

				# testing the dynamic programming problem with example
				# the optimal subset for the above example are items 3 and 4
				SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__     :     Optional[Any]		    =       knapsack_with_example_solution(w, wt, val)
				assert optimal_solution == 8
				assert optimal_subset == {3, 4}
				print("optimal_value = ", optimal_solution)
				print("An optimal subset corresponding to the optimal value", optimal_subset)






from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
				import torch

if is_torch_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm


SCREAMING_SNAKE_CASE__     :     int		    =       logging.get_logger(__name__)



@dataclass
class       a_       (     SCREAMING_SNAKE_CASE__     ):
	A    							= [
	    '''no_inference''',
	    '''no_cuda''',
	    '''no_tpu''',
	    '''no_speed''',
	    '''no_memory''',
	    '''no_env_print''',
	    '''no_multi_process''',
	]





	def __init__(							self      ,     **SCREAMING_SNAKE_CASE      )  ->					Dict:




				"""simple docstring"""



				for deprecated_arg in self.deprecated_args:
							if deprecated_arg in kwargs:
										SCREAMING_SNAKE_CASE_								=						deprecated_arg[3:]
										setattr(self      ,     SCREAMING_SNAKE_CASE      ,     not kwargs.pop(SCREAMING_SNAKE_CASE      )      )
										logger.warning(
										    f'{deprecated_arg} is depreciated. Please use --no_{positive_arg} or'
										    f' {positive_arg}={kwargs[positive_arg]}'      )

				SCREAMING_SNAKE_CASE_								=						kwargs.pop('torchscript'      ,     self.torchscript      )
				SCREAMING_SNAKE_CASE_								=						kwargs.pop('torch_xla_tpu_print_metrics'      ,     self.torch_xla_tpu_print_metrics      )
				SCREAMING_SNAKE_CASE_								=						kwargs.pop('fp16_opt_level'      ,     self.fpaa_opt_level      )
				super().__init__(**SCREAMING_SNAKE_CASE      )

	A    							= field(default=SCREAMING_SNAKE_CASE__  ,    metadata={'''help''': '''Trace the models using torchscript'''}     )
	A    							= field(default=SCREAMING_SNAKE_CASE__  ,    metadata={'''help''': '''Print Xla/PyTorch tpu metrics'''}     )
	A    							= field(
	    default='''O1'''  ,    metadata={
	        '''help''': (
	            '''For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\']. '''
	            '''See details at https://nvidia.github.io/apex/amp.html'''
	        )
	    }  ,    )





	@cached_property
	def 						A_(							self      )  ->					Tuple["torch.device", int]:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				logger.info('PyTorch: setting up devices'      )
				if not self.cuda:
							SCREAMING_SNAKE_CASE_								=						torch.device('cpu'      )
							SCREAMING_SNAKE_CASE_								=						0
				elif is_torch_tpu_available():
							SCREAMING_SNAKE_CASE_								=						xm.xla_device()
							SCREAMING_SNAKE_CASE_								=						0
				else:
							SCREAMING_SNAKE_CASE_								=						torch.device('cuda' if torch.cuda.is_available() else 'cpu'      )
							SCREAMING_SNAKE_CASE_								=						torch.cuda.device_count()
				return device, n_gpu





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




				"""simple docstring"""



				return is_torch_tpu_available() and self.tpu





	@property
	def 						A_(							self      )  ->					int:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				# TODO(PVP): currently only single GPU is supported
				return torch.cuda.current_device()





	@property
	def 						A_(							self      )  ->					"torch.device":




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				return self._setup_devices[0]





	@property
	def 						A_(							self      )  ->					Optional[Any]:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				return self._setup_devices[1]





	@property
	def 						A_(							self      )  ->					Dict:




				"""simple docstring"""



				return self.n_gpu > 0
