'''simple docstring'''






def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			List[Any]   ,		__snake_case							:			List[str]				):
     _A    		=  0
     _A    		=  len(__snake_case				) - 1

     while left <= right:
          # avoid divided by 0 during interpolation
          if sorted_collection[left] == sorted_collection[right]:
               if sorted_collection[left] == item:
                    return left
               else:
                    return None

          _A    		=  left + ((item - sorted_collection[left]) * (right - left)) // (
              sorted_collection[right] - sorted_collection[left]
          )

          # out of range check
          if point < 0 or point >= len(__snake_case				):
               return None

          _A    		=  sorted_collection[point]
          if current_item == item:
               return point
          else:
               if point < left:
                    _A    		=  left
                    _A    		=  point
               elif point > right:
                    _A    		=  right
                    _A    		=  point
               else:
                    if item < current_item:
                         _A    		=  point - 1
                    else:
                         _A    		=  point + 1
     return None





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Any   ,		__snake_case							:			int   ,		__snake_case							:			Dict   ,		__snake_case							:			List[str]				):

     # avoid divided by 0 during interpolation
     if sorted_collection[left] == sorted_collection[right]:
          if sorted_collection[left] == item:
               return left
          else:
               return None

     _A    		=  left + ((item - sorted_collection[left]) * (right - left)) // (
         sorted_collection[right] - sorted_collection[left]
     )

     # out of range check
     if point < 0 or point >= len(__snake_case				):
          return None

     if sorted_collection[point] == item:
          return point
     elif point < left:
          return interpolation_search_by_recursion(__snake_case   ,		__snake_case   ,		__snake_case   ,		__snake_case				)
     elif point > right:
          return interpolation_search_by_recursion(__snake_case   ,		__snake_case   ,		__snake_case   ,		__snake_case				)
     else:
          if sorted_collection[point] > item:
               return interpolation_search_by_recursion(
                   __snake_case   ,		__snake_case   ,		__snake_case   ,		point - 1				)
          else:
               return interpolation_search_by_recursion(
                   __snake_case   ,		__snake_case   ,		point + 1   ,		__snake_case				)





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			Any				):
     if collection != sorted(__snake_case				):
          raise ValueError('Collection must be ascending sorted'				)
     return True


if __name__ == "__main__":
   import sys
   _UpperCAmelCase    :     int         =       0
   if debug == 1:
      _UpperCAmelCase    :     Optional[int]         =       [10, 30, 40, 45, 50, 66, 77, 93]
      try:
         __assert_sorted(collection)
      except ValueError:
         sys.exit('''Sequence must be ascending sorted to apply interpolation search''')
      _UpperCAmelCase    :     str         =       67

   _UpperCAmelCase    :     Any         =       interpolation_search(collection, target)
   if result is not None:
      print(F'''{target} found at positions: {result}''')
   else:
      print('''Not found''')




'''simple docstring'''






_UpperCAmelCase    :     Any         =       '''0.21.0'''

from .accelerator import Accelerator
from .big_modeling import (
    cpu_offload,
    cpu_offload_with_hook,
    disk_offload,
    dispatch_model,
    init_empty_weights,
    init_on_device,
    load_checkpoint_and_dispatch,
)
from .data_loader import skip_first_batches
from .launchers import debug_launcher, notebook_launcher
from .state import PartialState
from .utils import (
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    FullyShardedDataParallelPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    find_executable_batch_size,
    infer_auto_device_map,
    is_rich_available,
    load_checkpoint_in_model,
    synchronize_rng_states,
)


if is_rich_available():
   from .utils import rich



