
"""simple docstring"""





from typing import List

import numpy as np







def 	__a     (		__lowerCamelCase  ):
   UpperCAmelCase_					:					Dict			     =    {key: len(__lowerCamelCase  ) for key, value in gen_kwargs.items() if isinstance(__lowerCamelCase,		__lowerCamelCase  )}
   if len(set(lists_lengths.values()  )  ) > 1:
      raise RuntimeError(
          (
              "Sharding is ambiguous for this dataset: "
              + "we found several data sources lists of different lengths, and we don't know over which list we should parallelize:\n"
              + "\n".join(f"""\t- key {key} has length {length}""" for key, length in lists_lengths.items()  )
              + "\nTo fix this, check the 'gen_kwargs' and make sure to use lists only for data sources, "
              + "and use tuples otherwise. In the end there should only be one single list, or several lists with the same length."
          )  )
   UpperCAmelCase_					:					List[str]			     =    max(lists_lengths.values(),		default=0  )
   return max(1,		__lowerCamelCase  )







def 	__a     (		__lowerCamelCase,		__lowerCamelCase  ):
   UpperCAmelCase_					:					Optional[int]			     =    []
   for group_idx in range(__lowerCamelCase  ):
      UpperCAmelCase_					:					Union[str, Any]			     =    num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
      if num_shards_to_add == 0:
         break
      UpperCAmelCase_					:					Optional[Any]			     =    shards_indices_per_group[-1].stop if shards_indices_per_group else 0
      UpperCAmelCase_					:					List[Any]			     =    range(__lowerCamelCase,		start + num_shards_to_add  )
      shards_indices_per_group.append(__lowerCamelCase  )
   return shards_indices_per_group







def 	__a     (		__lowerCamelCase,		__lowerCamelCase  ):
   UpperCAmelCase_					:					Any			     =    _number_of_shards_in_gen_kwargs(__lowerCamelCase  )
   if num_shards == 1:
      return [dict(__lowerCamelCase  )]
   else:
      UpperCAmelCase_					:					Any			     =    _distribute_shards(num_shards=__lowerCamelCase,		max_num_jobs=__lowerCamelCase  )
      return [
          {
              key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
              if isinstance(__lowerCamelCase,		__lowerCamelCase  )
              else value
              for key, value in gen_kwargs.items()
          }
          for group_idx in range(len(__lowerCamelCase  )  )
      ]







def 	__a     (		__lowerCamelCase  ):
   return {
       key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
       if isinstance(gen_kwargs_list[0][key],		__lowerCamelCase  )
       else gen_kwargs_list[0][key]
       for key in gen_kwargs_list[0]
   }







def 	__a     (		__lowerCamelCase,		__lowerCamelCase  ):
   UpperCAmelCase_					:					Union[str, Any]			     =    {len(__lowerCamelCase  ) for value in gen_kwargs.values() if isinstance(__lowerCamelCase,		__lowerCamelCase  )}
   UpperCAmelCase_					:					List[str]			     =    {}
   for size in list_sizes:
      UpperCAmelCase_					:					Tuple			     =    list(range(__lowerCamelCase  )  )
      rng.shuffle(indices_per_size[size]  )
   # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
   UpperCAmelCase_					:					Optional[int]			     =    dict(__lowerCamelCase  )
   for key, value in shuffled_kwargs.items():
      if isinstance(__lowerCamelCase,		__lowerCamelCase  ):
         UpperCAmelCase_					:					str			     =    [value[i] for i in indices_per_size[len(__lowerCamelCase  )]]
   return shuffled_kwargs





'''simple docstring'''



def    a__       (  a__      ,    a__						):




     """simple docstring"""


     _enforce_args(a__      ,    a__						)
     if n == 0:
          return 0
     __SCREAMING_SNAKE_CASE     =      float("""-inf"""						)
     for i in range(1      ,    n + 1						):
          __SCREAMING_SNAKE_CASE     =      max(
              a__      ,    prices[i - 1] + naive_cut_rod_recursive(n - i      ,    a__						)						)

     return max_revue







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     _enforce_args(a__      ,    a__						)
     __SCREAMING_SNAKE_CASE     =      [float("""-inf"""						) for _ in range(n + 1						)]
     return _top_down_cut_rod_recursive(a__      ,    a__      ,    a__						)







def    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


     if max_rev[n] >= 0:
          return max_rev[n]
     elif n == 0:
          return 0
     else:
          __SCREAMING_SNAKE_CASE     =      float("""-inf"""						)
          for i in range(1      ,    n + 1						):
               __SCREAMING_SNAKE_CASE     =      max(
                   a__      ,    prices[i - 1] + _top_down_cut_rod_recursive(n - i      ,    a__      ,    a__						)      ,    )

          __SCREAMING_SNAKE_CASE     =      max_revenue

     return max_rev[n]







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     _enforce_args(a__      ,    a__						)

     # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
     # length 0.
     __SCREAMING_SNAKE_CASE     =      [float("""-inf"""						) for _ in range(n + 1						)]
     __SCREAMING_SNAKE_CASE     =      0

     for i in range(1      ,    n + 1						):
          __SCREAMING_SNAKE_CASE     =      max_rev[i]
          for j in range(1      ,    i + 1						):
               __SCREAMING_SNAKE_CASE     =      max(a__      ,    prices[j - 1] + max_rev[i - j]						)

          __SCREAMING_SNAKE_CASE     =      max_revenue_i

     return max_rev[n]







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     if n < 0:
          __SCREAMING_SNAKE_CASE     =      F'n must be greater than or equal to 0. Got n = {n}'
          raise ValueError(a__						)

     if n > len(a__						):
          __SCREAMING_SNAKE_CASE     =      (
              """Each integral piece of rod must have a corresponding price. """
              F'Got n = {n} but length of prices = {len(a__						)}'
          )
          raise ValueError(a__						)







def    a__       (  ):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      [6, 10, 12, 15, 20, 23]
     __SCREAMING_SNAKE_CASE     =      len(a__						)

     # the best revenue comes from cutting the rod into 6 pieces, each
     # of length 1 resulting in a revenue of 6 * 6 = 36.
     __SCREAMING_SNAKE_CASE     =      36

     __SCREAMING_SNAKE_CASE     =      top_down_cut_rod(a__      ,    a__						)
     __SCREAMING_SNAKE_CASE     =      bottom_up_cut_rod(a__      ,    a__						)
     __SCREAMING_SNAKE_CASE     =      naive_cut_rod_recursive(a__      ,    a__						)

     assert expected_max_revenue == max_rev_top_down
     assert max_rev_top_down == max_rev_bottom_up
     assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
  main()






