


def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : Optional[Any]      ,					SCREAMING_SNAKE_CASE__      : Any      ,					SCREAMING_SNAKE_CASE__      : List[str]      ,					SCREAMING_SNAKE_CASE__      : str    ):
     global f  # a global dp table for knapsack
     if f[i][j] < 0:
          if j < wt[i - 1]:
               __UpperCamelCase   							=mf_knapsack(i - 1      ,					SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    )
          else:
               __UpperCamelCase   							=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]      ,					)
          __UpperCamelCase   							=val
     return f[i][j]

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : Any      ,					SCREAMING_SNAKE_CASE__      : Optional[int]      ,					SCREAMING_SNAKE_CASE__      : List[str]      ,					SCREAMING_SNAKE_CASE__      : Dict    ):
     __UpperCamelCase   							=[[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_:
                    __UpperCamelCase   							=max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]      ,					dp[i - 1][w_]    )
               else:
                    __UpperCamelCase   							=dp[i - 1][w_]

     return dp[n][w_], dp

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int      ,					SCREAMING_SNAKE_CASE__      : str      ,					SCREAMING_SNAKE_CASE__      : str    ):
     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'    )

     __UpperCamelCase   							=len(SCREAMING_SNAKE_CASE__    )
     if num_items != len(SCREAMING_SNAKE_CASE__    ):
          __UpperCamelCase   							=(
              '''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__    ):
               __UpperCamelCase   							=(
                   '''All weights must be integers but got weight of '''
                   F'type {type(wt[i]    )} at index {i}'
               )
               raise TypeError(SCREAMING_SNAKE_CASE__    )

     __UpperCamelCase   							=knapsack(SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__      ,					SCREAMING_SNAKE_CASE__    )
     __UpperCamelCase   							=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 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : Union[str, Any]      ,					SCREAMING_SNAKE_CASE__      : Dict      ,					SCREAMING_SNAKE_CASE__      : Union[str, Any]      ,					SCREAMING_SNAKE_CASE__      : List[Any]      ,					SCREAMING_SNAKE_CASE__      : Any    ):
     # for the current item i at a maximum weight j to be part of an optimal subset,
     # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
     # where i - 1 means considering only the previous items at the given maximum weight
     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__":
   _A			=						[3, 2, 4, 4]
   _A			=						[4, 3, 2, 3]
   _A			=						4
   _A			=						6
   _A			=						[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
   _A	,					_A			=						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
   _A	,					_A			=						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)









import inspect
import os
import unittest
from dataclasses import dataclass

import torch

from accelerate import Accelerator, DistributedDataParallelKwargs, GradScalerKwargs
from accelerate.state import AcceleratorState
from accelerate.test_utils import execute_subprocess_async, require_cuda, require_multi_gpu
from accelerate.utils import KwargsHandler






@dataclass
class    UpperCAmelCase__	( A_		):



    """simple docstring"""






    UpperCAmelCase__						:		int              =  0
    UpperCAmelCase__						:		bool              =  False
    UpperCAmelCase__						:		float              =  3.0






class    UpperCAmelCase__	( unittest.TestCase		):



    """simple docstring"""






    def _a (      self   )  ->	Any:
         # If no defaults are changed, `to_kwargs` returns an empty dict.
         self.assertDictEqual(MockClass().to_kwargs() ,       {}   )
         self.assertDictEqual(MockClass(a=2   ).to_kwargs() ,       {'a': 2}   )
         self.assertDictEqual(MockClass(a=2 ,       b=A_   ).to_kwargs() ,       {'a': 2, 'b': True}   )
         self.assertDictEqual(MockClass(a=2 ,       c=2.25   ).to_kwargs() ,       {'a': 2, 'c': 2.25}   )






    @require_cuda
    def _a (      self   )  ->	Union[str, Any]:
         # If no defaults are changed, `to_kwargs` returns an empty dict.
         __UpperCamelCase   							=GradScalerKwargs(init_scale=1024 ,       growth_factor=2   )
         AcceleratorState._reset_state()
         __UpperCamelCase   							=Accelerator(mixed_precision='fp16' ,       kwargs_handlers=[scaler_handler]   )
         print(accelerator.use_fpaa   )
         __UpperCamelCase   							=accelerator.scaler

         # Check the kwargs have been applied
         self.assertEqual(scaler._init_scale ,       1024.0   )
         self.assertEqual(scaler._growth_factor ,       2.0   )

         # Check the other values are at the default
         self.assertEqual(scaler._backoff_factor ,       0.5   )
         self.assertEqual(scaler._growth_interval ,       2000   )
         self.assertEqual(scaler._enabled ,       A_   )






    @require_multi_gpu
    def _a (      self   )  ->	Optional[int]:
         __UpperCamelCase   							=['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', inspect.getfile(self.__class__   )]
         execute_subprocess_async(A_ ,       env=os.environ.copy()   )


if __name__ == "__main__":
   _A			=						DistributedDataParallelKwargs(bucket_cap_mb=15, find_unused_parameters=True)
   _A			=						Accelerator(kwargs_handlers=[ddp_scaler])
   _A			=						torch.nn.Linear(100, 200)
   _A			=						accelerator.prepare(model)

   # Check the values changed in kwargs
   _A			=						''
   _A			=						model.bucket_bytes_cap // (1024 * 1024)
   if observed_bucket_cap_map != 15:
      error_msg += f"Kwargs badly passed, should have `15` but found {observed_bucket_cap_map}.\n"
   if model.find_unused_parameters is not True:
      error_msg += f"Kwargs badly passed, should have `True` but found {model.find_unused_parameters}.\n"

   # Check the values of the defaults
   if model.dim != 0:
      error_msg += f"Default value not respected, should have `0` but found {model.dim}.\n"
   if model.broadcast_buffers is not True:
      error_msg += f"Default value not respected, should have `True` but found {model.broadcast_buffers}.\n"
   if model.gradient_as_bucket_view is not False:
      error_msg += f"Default value not respected, should have `False` but found {model.gradient_as_bucket_view}.\n"

   # Raise error at the end to make sure we don't stop at the first failure.
   if len(error_msg) > 0:
      raise ValueError(error_msg)





