






'''simple docstring'''





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






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__				,     lowercase__):
 lowerCamelCase__  =     [[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_:
    lowerCamelCase__  =     max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]				,     dp[i - 1][w_])
   else:
    lowerCamelCase__  =     dp[i - 1][w_]

 return dp[n][w_], dp






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__):
 if not (isinstance(lowercase__				,     (list, tuple)) and isinstance(lowercase__				,     (list, tuple))):
  raise ValueError(
      "Both the weights and values vectors must be either lists or tuples")

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

 lowerCamelCase__  ,	lowerCamelCase__  =     knapsack(lowercase__				,     lowercase__				,     lowercase__				,     lowercase__)
 lowerCamelCase__  =     set()
 _construct_solution(lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__)

 return optimal_val, example_optional_set






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__):
 # 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(lowercase__				,     lowercase__				,     i - 1				,     lowercase__				,     lowercase__)
  else:
   optimal_set.add(lowercase__)
   _construct_solution(lowercase__				,     lowercase__				,     i - 1				,     j - wt[i - 1]				,     lowercase__)


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





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


__A							:							Union[str, Any]  							=		{
    """configuration_layoutlmv2""": ["""LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LayoutLMv2Config"""],
    """processing_layoutlmv2""": ["""LayoutLMv2Processor"""],
    """tokenization_layoutlmv2""": ["""LayoutLMv2Tokenizer"""],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A							:							Optional[Any]  							=		["""LayoutLMv2TokenizerFast"""]

try:
 if not is_vision_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A							:							List[Any]  							=		["""LayoutLMv2FeatureExtractor"""]
 __A							:							List[Any]  							=		["""LayoutLMv2ImageProcessor"""]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A							:							Any  							=		[
     """LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """LayoutLMv2ForQuestionAnswering""",
     """LayoutLMv2ForSequenceClassification""",
     """LayoutLMv2ForTokenClassification""",
     """LayoutLMv2Layer""",
     """LayoutLMv2Model""",
     """LayoutLMv2PreTrainedModel""",
 ]

if TYPE_CHECKING:
 from .configuration_layoutlmva import LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP, LayoutLMvaConfig
 from .processing_layoutlmva import LayoutLMvaProcessor
 from .tokenization_layoutlmva import LayoutLMvaTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_layoutlmva_fast import LayoutLMvaTokenizerFast

 try:
  if not is_vision_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .feature_extraction_layoutlmva import LayoutLMvaFeatureExtractor, LayoutLMvaImageProcessor

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_layoutlmva import (
      LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST,
      LayoutLMvaForQuestionAnswering,
      LayoutLMvaForSequenceClassification,
      LayoutLMvaForTokenClassification,
      LayoutLMvaLayer,
      LayoutLMvaModel,
      LayoutLMvaPreTrainedModel,
  )
else:
 import sys

 __A							:							Tuple  							=		_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

