






def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			str:

     '''simple docstring'''
     global f  # a global dp table for knapsack
     if f[i][j] < 0:
          if j < wt[i - 1]:
               UpperCAmelCase__      :  str				      =			mf_knapsack(i - 1 ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       )
          else:
               UpperCAmelCase__      :  str				      =			max(
                   mf_knapsack(i - 1 ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ,							mf_knapsack(i - 1 ,							__lowerCamelCase ,							__lowerCamelCase ,							j - wt[i - 1]       ) + val[i - 1] ,							)
          UpperCAmelCase__      :  Tuple				      =			val
     return f[i][j]





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			str:

     '''simple docstring'''
     UpperCAmelCase__      :  Tuple				      =			[[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__      :  Optional[Any]				      =			max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] ,							dp[i - 1][w_]       )
               else:
                    UpperCAmelCase__      :  Dict				      =			dp[i - 1][w_]

     return dp[n][w_], dp





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			Dict:

     '''simple docstring'''
     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"""       )

     UpperCAmelCase__      :  Optional[Any]				      =			len(__lowerCamelCase       )
     if num_items != len(__lowerCamelCase       ):
          UpperCAmelCase__      :  Optional[int]				      =			(
              """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       ):
               UpperCAmelCase__      :  List[str]				      =			(
                   """All weights must be integers but got weight of """
                   F"type {type(wt[i]       )} at index {i}"
               )
               raise TypeError(__lowerCamelCase       )

     UpperCAmelCase__      ,		UpperCAmelCase__      :  Any				      =			knapsack(__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       )
     UpperCAmelCase__      :  set				      =			set()
     _construct_solution(__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       )

     return optimal_val, example_optional_set





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase       ) ->			int:

     '''simple docstring'''
     # 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__":
      SCREAMING_SNAKE_CASE__		:							List[str] 				=				[3, 2, 4, 4]
      SCREAMING_SNAKE_CASE__		:							Tuple 				=				[4, 3, 2, 3]
      SCREAMING_SNAKE_CASE__		:							Any 				=				4
      SCREAMING_SNAKE_CASE__		:							str 				=				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[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
      SCREAMING_SNAKE_CASE__				,			SCREAMING_SNAKE_CASE__		:							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 pathlib import PurePosixPath
from typing import Optional

import fsspec
from fsspec import AbstractFileSystem
from huggingface_hub.hf_api import DatasetInfo

from ..utils.file_utils import get_authentication_headers_for_url
from ..utils.hub import hf_hub_url







class __a			( _snake_case      ):
   __UpperCamelCase :			Any						   =						''
   __UpperCamelCase :			int						   =						'hf-legacy'  # "hf://"" is reserved for hffs





   def __init__(       self					:      Any					,lowerCamelCase					:      Optional[DatasetInfo] = None					,lowerCamelCase					:      Optional[str] = None					,**lowerCamelCase					:      Dict					,):

      '''simple docstring'''

      super().__init__(self					,**lowerCamelCase     )
      __SCREAMING_SNAKE_CASE   				=							repo_info
      __SCREAMING_SNAKE_CASE   				=							token
      __SCREAMING_SNAKE_CASE   				=							None





   def   UpperCAmelCase__  (       self					:      Optional[int]     ):

      '''simple docstring'''

      if self.dir_cache is None:
         __SCREAMING_SNAKE_CASE   				=							{}
         for hf_file in self.repo_info.siblings:
            # TODO(QL): add sizes
            __SCREAMING_SNAKE_CASE   				=							{
                """name""": hf_file.rfilename,
                """size""": None,
                """type""": """file""",
            }
            self.dir_cache.update(
                {
                    str(lowerCamelCase     ): {"""name""": str(lowerCamelCase     ), """size""": None, """type""": """directory"""}
                    for d in list(PurePosixPath(hf_file.rfilename     ).parents     )[:-1]
                }     )





   def   UpperCAmelCase__  (       self					:      List[Any]					,lowerCamelCase					:      str					,lowerCamelCase					:      str = "rb"					,**lowerCamelCase					:      Optional[Any]					,):

      '''simple docstring'''

      if not isinstance(self.repo_info					,lowerCamelCase     ):
         raise NotImplementedError(f"""Open is only implemented for dataset repositories, but got {self.repo_info}"""     )
      __SCREAMING_SNAKE_CASE   				=							hf_hub_url(self.repo_info.id					,lowerCamelCase					,revision=self.repo_info.sha     )
      return fsspec.open(
          lowerCamelCase					,mode=lowerCamelCase					,headers=get_authentication_headers_for_url(lowerCamelCase					,use_auth_token=self.token     )					,client_kwargs={"""trust_env""": True}					,).open()





   def   UpperCAmelCase__  (       self					:      Tuple					,lowerCamelCase					:      Any					,**lowerCamelCase					:      Optional[Any]     ):

      '''simple docstring'''

      self._get_dirs()
      __SCREAMING_SNAKE_CASE   				=							self._strip_protocol(lowerCamelCase     )
      if path in self.dir_cache:
         return self.dir_cache[path]
      else:
         raise FileNotFoundError(lowerCamelCase     )





   def   UpperCAmelCase__  (       self					:      str					,lowerCamelCase					:      Any					,lowerCamelCase					:      str=False					,**lowerCamelCase					:      Any     ):

      '''simple docstring'''

      self._get_dirs()
      __SCREAMING_SNAKE_CASE   				=							PurePosixPath(path.strip("""/"""     )     )
      __SCREAMING_SNAKE_CASE   				=							{}
      for p, f in self.dir_cache.items():
         __SCREAMING_SNAKE_CASE   				=							PurePosixPath(p.strip("""/"""     )     )
         __SCREAMING_SNAKE_CASE   				=							p.parent
         if root == path:
            __SCREAMING_SNAKE_CASE   				=							f
      __SCREAMING_SNAKE_CASE   				=							list(paths.values()     )
      if detail:
         return out
      else:
         return sorted(f["""name"""] for f in out     )





