


'''simple docstring'''

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("""ignore""", category=UserWarning, module="""torch.optim.lr_scheduler""")





class      snake_case    :





  """simple docstring"""




  def __init__(    self			,  UpperCamelCase			,  UpperCamelCase			,  UpperCamelCase = True			,  UpperCamelCase = False     ):







   """simple docstring"""
   lowerCamelCase_      =  scheduler
   lowerCamelCase_      =  optimizers if isinstance(_lowerCamelCase			,  (list, tuple)     ) else [optimizers]
   lowerCamelCase_      =  split_batches
   lowerCamelCase_      =  step_with_optimizer
   lowerCamelCase_      =  GradientState()






  def   snake_case		(    self			,  *UpperCamelCase			,  **UpperCamelCase     ):







   """simple docstring"""
   if not self.step_with_optimizer:
    # No link between scheduler and optimizer -> just step
    self.scheduler.step(*_lowerCamelCase			,  **_lowerCamelCase     )
    return

   # Otherwise, first make sure the optimizer was stepped.
   if not self.gradient_state.sync_gradients:
    if self.gradient_state.adjust_scheduler:
     self.scheduler._step_count += 1
    return

   for opt in self.optimizers:
    if opt.step_was_skipped:
     return
   if self.split_batches:
    # Split batches -> the training dataloader batch size is not changed so one step per training step
    self.scheduler.step(*_lowerCamelCase			,  **_lowerCamelCase     )
   else:
    # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
    # num_processes steps per training step
    lowerCamelCase_      =  AcceleratorState().num_processes
    for _ in range(_lowerCamelCase     ):
     # Special case when using OneCycle and `drop_last` was not used
     if hasattr(self.scheduler			,  "total_steps"     ):
      if self.scheduler._step_count <= self.scheduler.total_steps:
       self.scheduler.step(*_lowerCamelCase			,  **_lowerCamelCase     )
     else:
      self.scheduler.step(*_lowerCamelCase			,  **_lowerCamelCase     )






  def   snake_case		(    self     ):







   """simple docstring"""
   return self.scheduler.get_last_lr()






  def   snake_case		(    self     ):







   """simple docstring"""
   return self.scheduler.state_dict()






  def   snake_case		(    self			,  UpperCamelCase     ):







   """simple docstring"""
   self.scheduler.load_state_dict(_lowerCamelCase     )






  def   snake_case		(    self     ):







   """simple docstring"""
   return self.scheduler.get_lr()







  def   snake_case		(    self			,  *UpperCamelCase			,  **UpperCamelCase     ):







   """simple docstring"""
   return self.scheduler.print_lr(*_lowerCamelCase			,  **_lowerCamelCase     )





"""simple docstring"""



from math import pow
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       int ,					)     ->					tuple[int, int]:
  if current_sum == needed_sum:
    # If the sum of the powers is equal to needed_sum, then we have a solution.
    solutions_count += 1
    return current_sum, solutions_count

  _snake_case					     =       int(pow(__lowerCamelCase ,					__lowerCamelCase		)		)
  if current_sum + i_to_n <= needed_sum:
    # If the sum of the powers is less than needed_sum, then continue adding powers.
    current_sum += i_to_n
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
    current_sum -= i_to_n
  if i_to_n < needed_sum:
    # If the power of i is less than needed_sum, then try with the next power.
    _snake_case     ,					_snake_case					     =       backtrack(
        __lowerCamelCase ,					__lowerCamelCase ,					current_number + 1 ,					__lowerCamelCase ,					__lowerCamelCase		)
  return current_sum, solutions_count
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int ,					__lowerCamelCase   :       int		)     ->					int:
  if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
    raise ValueError(
        '''Invalid input\n'''
        '''needed_sum must be between 1 and 1000, power between 2 and 10.'''		)

  return backtrack(__lowerCamelCase ,					__lowerCamelCase ,					1 ,					0 ,					0		)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()



