

"""simple docstring"""


def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				Dict:
      global f  # a global dp table for knapsack
      if f[i][j] < 0:
            if j < wt[i - 1]:
                  SCREAMING_SNAKE_CASE__   :      Any      		=	mf_knapsack(i - 1  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)
            else:
                  SCREAMING_SNAKE_CASE__   :      Any      		=	max(
                      mf_knapsack(i - 1  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)  ,					mf_knapsack(i - 1  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					j - wt[i - 1]							) + val[i - 1]  ,					)
            SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	val
      return f[i][j]




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				Dict:
      SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	[[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__   :      int      		=	max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]  ,					dp[i - 1][w_]							)
                  else:
                        SCREAMING_SNAKE_CASE__   :      List[Any]      		=	dp[i - 1][w_]

      return dp[n][w_], dp




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

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

      SCREAMING_SNAKE_CASE__		,		SCREAMING_SNAKE_CASE__   :      Any      		=	knapsack(__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)
      SCREAMING_SNAKE_CASE__   :      set      		=	set()
      _construct_solution(__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)

      return optimal_val, example_optional_set




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				int:
      # 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(__lowerCAmelCase  ,					__lowerCAmelCase  ,					i - 1  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)
            else:
                  optimal_set.add(__lowerCAmelCase							)
                  _construct_solution(__lowerCAmelCase  ,					__lowerCAmelCase  ,					i - 1  ,					j - wt[i - 1]  ,					__lowerCAmelCase							)


if __name__ == "__main__":
  a					:List[Any]    = [3, 2, 4, 4]
  a					:int    = [4, 3, 2, 3]
  a					:List[str]    = 4
  a					:List[str]    = 6
  a					:Dict    = [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
  a    ,a					: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
  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_flax_available,
    is_tf_available,
    is_torch_available,
)


a					:Any    = {
    "configuration_roberta_prelayernorm": [
        "ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "RobertaPreLayerNormConfig",
        "RobertaPreLayerNormOnnxConfig",
    ],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  a					:Union[str, Any]    = [
      "ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
      "RobertaPreLayerNormForCausalLM",
      "RobertaPreLayerNormForMaskedLM",
      "RobertaPreLayerNormForMultipleChoice",
      "RobertaPreLayerNormForQuestionAnswering",
      "RobertaPreLayerNormForSequenceClassification",
      "RobertaPreLayerNormForTokenClassification",
      "RobertaPreLayerNormModel",
      "RobertaPreLayerNormPreTrainedModel",
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  a					:Optional[Any]    = [
      "TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
      "TFRobertaPreLayerNormForCausalLM",
      "TFRobertaPreLayerNormForMaskedLM",
      "TFRobertaPreLayerNormForMultipleChoice",
      "TFRobertaPreLayerNormForQuestionAnswering",
      "TFRobertaPreLayerNormForSequenceClassification",
      "TFRobertaPreLayerNormForTokenClassification",
      "TFRobertaPreLayerNormMainLayer",
      "TFRobertaPreLayerNormModel",
      "TFRobertaPreLayerNormPreTrainedModel",
  ]

try:
  if not is_flax_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  a					:List[Any]    = [
      "FlaxRobertaPreLayerNormForCausalLM",
      "FlaxRobertaPreLayerNormForMaskedLM",
      "FlaxRobertaPreLayerNormForMultipleChoice",
      "FlaxRobertaPreLayerNormForQuestionAnswering",
      "FlaxRobertaPreLayerNormForSequenceClassification",
      "FlaxRobertaPreLayerNormForTokenClassification",
      "FlaxRobertaPreLayerNormModel",
      "FlaxRobertaPreLayerNormPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_roberta_prelayernorm import (
      ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
      RobertaPreLayerNormConfig,
      RobertaPreLayerNormOnnxConfig,
  )

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_roberta_prelayernorm import (
        ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
        RobertaPreLayerNormForCausalLM,
        RobertaPreLayerNormForMaskedLM,
        RobertaPreLayerNormForMultipleChoice,
        RobertaPreLayerNormForQuestionAnswering,
        RobertaPreLayerNormForSequenceClassification,
        RobertaPreLayerNormForTokenClassification,
        RobertaPreLayerNormModel,
        RobertaPreLayerNormPreTrainedModel,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_roberta_prelayernorm import (
        TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFRobertaPreLayerNormForCausalLM,
        TFRobertaPreLayerNormForMaskedLM,
        TFRobertaPreLayerNormForMultipleChoice,
        TFRobertaPreLayerNormForQuestionAnswering,
        TFRobertaPreLayerNormForSequenceClassification,
        TFRobertaPreLayerNormForTokenClassification,
        TFRobertaPreLayerNormMainLayer,
        TFRobertaPreLayerNormModel,
        TFRobertaPreLayerNormPreTrainedModel,
    )

  try:
    if not is_flax_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flax_roberta_prelayernorm import (
        FlaxRobertaPreLayerNormForCausalLM,
        FlaxRobertaPreLayerNormForMaskedLM,
        FlaxRobertaPreLayerNormForMultipleChoice,
        FlaxRobertaPreLayerNormForQuestionAnswering,
        FlaxRobertaPreLayerNormForSequenceClassification,
        FlaxRobertaPreLayerNormForTokenClassification,
        FlaxRobertaPreLayerNormModel,
        FlaxRobertaPreLayerNormPreTrainedModel,
    )

else:
  import sys

  a					:Optional[int]    = _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




