





def    __snake_case  (    _lowerCAmelCase       :       str , _lowerCAmelCase       :       int , _lowerCAmelCase       :       str , _lowerCAmelCase       :       Dict		)       ->  List[str]:
   global f  # a global dp table for knapsack
   if f[i][j] < 0:
      if j < wt[i - 1]:
         A_    : Union[str, Any]								=	mf_knapsack(i - 1 , _snake_case , _snake_case , _snake_case		)
      else:
         A_    : Any								=	max(
             mf_knapsack(i - 1 , _snake_case , _snake_case , _snake_case		) , mf_knapsack(i - 1 , _snake_case , _snake_case , j - wt[i - 1]		) + val[i - 1] , )
      A_    : Dict								=	val
   return f[i][j]

def    __snake_case  (    _lowerCAmelCase       :       Union[str, Any] , _lowerCAmelCase       :       int , _lowerCAmelCase       :       List[Any] , _lowerCAmelCase       :       int		)       ->  Optional[int]:
   A_    : Optional[int]								=	[[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_:
            A_    : Union[str, Any]								=	max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] , dp[i - 1][w_]		)
         else:
            A_    : Tuple								=	dp[i - 1][w_]

   return dp[n][w_], dp

def    __snake_case  (    _lowerCAmelCase       :       int , _lowerCAmelCase       :       list , _lowerCAmelCase       :       list		)       ->  List[Any]:
   if not (isinstance(_snake_case , (list, tuple)		) and isinstance(_snake_case , (list, tuple)		)):
      raise ValueError(
          "Both the weights and values vectors must be either lists or tuples"		)

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

   A_    : List[str]								=	knapsack(_snake_case , _snake_case , _snake_case , _snake_case		)
   A_    : set								=	set()
   _construct_solution(_snake_case , _snake_case , _snake_case , _snake_case , _snake_case		)

   return optimal_val, example_optional_set

def    __snake_case  (    _lowerCAmelCase       :       list , _lowerCAmelCase       :       list , _lowerCAmelCase       :       int , _lowerCAmelCase       :       int , _lowerCAmelCase       :       set		)       ->  Tuple:
   # 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(_snake_case , _snake_case , i - 1 , _snake_case , _snake_case		)
      else:
         optimal_set.add(_snake_case		)
         _construct_solution(_snake_case , _snake_case , i - 1 , j - wt[i - 1] , _snake_case		)


if __name__ == "__main__":
 _lowerCAmelCase							:					Optional[int]		    =		[3, 2, 4, 4]
 _lowerCAmelCase							:					str		    =		[4, 3, 2, 3]
 _lowerCAmelCase							:					List[str]		    =		4
 _lowerCAmelCase							:					Optional[Any]		    =		6
 _lowerCAmelCase							:					Union[str, Any]		    =		[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 _lowerCAmelCase							:					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
 _lowerCAmelCase							:					int		    =		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)




"""simple docstring"""





import gc
import unittest

from diffusers import FlaxDPMSolverMultistepScheduler, FlaxStableDiffusionPipeline
from diffusers.utils import is_flax_available, slow
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
 import jax
 import jax.numpy as jnp
 from flax.jax_utils import replicate
 from flax.training.common_utils import shard



@slow
@require_flax
class 						snake_case_(				unittest.TestCase	):






     def    lowerCamelCase__   (		self     :    int ):
           # clean up the VRAM after each test
           super().tearDown()
           gc.collect()






     def    lowerCamelCase__   (		self     :    Optional[Any] ):
           lowerCAmelCase,					lowerCAmelCase    :		Optional[int]				=      FlaxStableDiffusionPipeline.from_pretrained(
               '''stabilityai/stable-diffusion-2'''    , revision='''bf16'''    , dtype=jnp.bfloataa    , )

           lowerCAmelCase    :		Optional[int]				=      '''A painting of a squirrel eating a burger'''
           lowerCAmelCase    :		List[str]				=      jax.device_count()
           lowerCAmelCase    :		Optional[int]				=      num_samples * [prompt]
           lowerCAmelCase    :		Any				=      sd_pipe.prepare_inputs(UpperCamelCase_ )

           lowerCAmelCase    :		Optional[int]				=      replicate(UpperCamelCase_ )
           lowerCAmelCase    :		Union[str, Any]				=      shard(UpperCamelCase_ )

           lowerCAmelCase    :		Optional[int]				=      jax.random.PRNGKey(0 )
           lowerCAmelCase    :		Optional[Any]				=      jax.random.split(UpperCamelCase_    , jax.device_count() )

           lowerCAmelCase    :		str				=      sd_pipe(UpperCamelCase_    , UpperCamelCase_    , UpperCamelCase_    , num_inference_steps=2_5    , jit=UpperCamelCase_ )[0]
           assert images.shape == (jax.device_count(), 1, 7_6_8, 7_6_8, 3)

           lowerCAmelCase    :		str				=      images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:] )
           lowerCAmelCase    :		List[str]				=      images[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

           lowerCAmelCase    :		Dict				=      jnp.asarray(jax.device_get(image_slice.flatten() ) )
           lowerCAmelCase    :		List[str]				=      jnp.array([0.4_238, 0.4_414, 0.4_395, 0.4_453, 0.4_629, 0.4_590, 0.4_531, 0.45_508, 0.4_512] )
           print(F'''output_slice: {output_slice}''' )
           assert jnp.abs(output_slice - expected_slice ).max() < 1E-2






     def    lowerCamelCase__   (		self     :    Union[str, Any] ):
           lowerCAmelCase    :		Union[str, Any]				=      '''stabilityai/stable-diffusion-2'''
           lowerCAmelCase,					lowerCAmelCase    :		Dict				=      FlaxDPMSolverMultistepScheduler.from_pretrained(UpperCamelCase_    , subfolder='''scheduler''' )
           lowerCAmelCase,					lowerCAmelCase    :		int				=      FlaxStableDiffusionPipeline.from_pretrained(
               UpperCamelCase_    , scheduler=UpperCamelCase_    , revision='''bf16'''    , dtype=jnp.bfloataa    , )
           lowerCAmelCase    :		List[Any]				=      scheduler_params

           lowerCAmelCase    :		List[Any]				=      '''A painting of a squirrel eating a burger'''
           lowerCAmelCase    :		Any				=      jax.device_count()
           lowerCAmelCase    :		int				=      num_samples * [prompt]
           lowerCAmelCase    :		int				=      sd_pipe.prepare_inputs(UpperCamelCase_ )

           lowerCAmelCase    :		Dict				=      replicate(UpperCamelCase_ )
           lowerCAmelCase    :		Tuple				=      shard(UpperCamelCase_ )

           lowerCAmelCase    :		int				=      jax.random.PRNGKey(0 )
           lowerCAmelCase    :		Optional[int]				=      jax.random.split(UpperCamelCase_    , jax.device_count() )

           lowerCAmelCase    :		Tuple				=      sd_pipe(UpperCamelCase_    , UpperCamelCase_    , UpperCamelCase_    , num_inference_steps=2_5    , jit=UpperCamelCase_ )[0]
           assert images.shape == (jax.device_count(), 1, 7_6_8, 7_6_8, 3)

           lowerCAmelCase    :		Any				=      images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:] )
           lowerCAmelCase    :		str				=      images[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

           lowerCAmelCase    :		Optional[int]				=      jnp.asarray(jax.device_get(image_slice.flatten() ) )
           lowerCAmelCase    :		Tuple				=      jnp.array([0.4_336, 0.42_969, 0.4_453, 0.4_199, 0.4_297, 0.4_531, 0.4_434, 0.4_434, 0.4_297] )
           print(F'''output_slice: {output_slice}''' )
           assert jnp.abs(output_slice - expected_slice ).max() < 1E-2


