


'''simple docstring'''






from typing import List

import numpy as np





def lowerCamelCase__      (						__lowerCamelCase	:							dict							):







   '''simple docstring'''




   _UpperCAmelCase       :       str							   ={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       :       Dict							   =max(lists_lengths.values()	,   default=0							)
   return max(1	,   __lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							int	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




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





def lowerCamelCase__      (						__lowerCamelCase	:							dict	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   _UpperCAmelCase       :       List[Any]							   =_number_of_shards_in_gen_kwargs(__lowerCamelCase							)
   if num_shards == 1:
      return [dict(__lowerCamelCase							)]
   else:
      _UpperCAmelCase       :       Union[str, 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 lowerCamelCase__      (						__lowerCamelCase	:							List[dict]							):







   '''simple docstring'''




   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 lowerCamelCase__      (						__lowerCamelCase	:							np.random.Generator	,   __lowerCamelCase	:							dict							):







   '''simple docstring'''




   _UpperCAmelCase       :       int							   ={len(__lowerCamelCase							) for value in gen_kwargs.values() if isinstance(__lowerCamelCase	,   __lowerCamelCase							)}
   _UpperCAmelCase       :       List[Any]							   ={}
   for size in list_sizes:
      _UpperCAmelCase       :       List[Any]							   =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       :       Any							   =dict(__lowerCamelCase							)
   for key, value in shuffled_kwargs.items():
      if isinstance(__lowerCamelCase	,   __lowerCamelCase							):
         _UpperCAmelCase       :       Optional[int]							   =[value[i] for i in indices_per_size[len(__lowerCamelCase							)]]
   return shuffled_kwargs





'''simple docstring'''






def lowerCamelCase__      (						__lowerCamelCase	:							int	,   __lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   def count_of_possible_combinations(__lowerCamelCase	:							int							) -> int:
      if target < 0:
         return 0
      if target == 0:
         return 1
      return sum(count_of_possible_combinations(target - item							) for item in array							)

   return count_of_possible_combinations(__lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							int	,   __lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   def count_of_possible_combinations_with_dp_array(
       __lowerCamelCase	:							int	,   __lowerCamelCase	:							list[int]							) -> int:
      if target < 0:
         return 0
      if target == 0:
         return 1
      if dp_array[target] != -1:
         return dp_array[target]
      _UpperCAmelCase       :       str							   =sum(
          count_of_possible_combinations_with_dp_array(target - item	,   __lowerCamelCase							)
          for item in array							)
      _UpperCAmelCase       :       Optional[Any]							   =answer
      return answer

   _UpperCAmelCase       :       int							   =[-1] * (target + 1)
   return count_of_possible_combinations_with_dp_array(__lowerCamelCase	,   __lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							int	,   __lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   _UpperCAmelCase       :       Tuple							   =[0] * (target + 1)
   _UpperCAmelCase       :       Dict							   =1

   for i in range(1	,   target + 1							):
      for j in range(__lowerCamelCase							):
         if i - array[j] >= 0:
            dp_array[i] += dp_array[i - array[j]]

   return dp_array[target]


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 lowercase							=3
 lowercase							=5
 lowercase							=[1, 2, 5]
 print(combination_sum_iv(n, array, target))

