


from copy import deepcopy

import torch
import torch.nn.functional as F
from torch.optim import AdamW
from torch.optim.lr_scheduler import LambdaLR
from torch.utils.data import DataLoader

from accelerate.accelerator import Accelerator
from accelerate.state import GradientState
from accelerate.test_utils import RegressionDataset, RegressionModel
from accelerate.utils import DistributedType, is_torch_version, set_seed




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)  ->    Tuple:
       for param, grad_param in zip(model_a.parameters()      ,							model_b.parameters()					):
              if not param.requires_grad:
                     continue
              if not did_step:
                     # Grads should not be in sync
                     assert (
                         torch.allclose(param.grad      ,							grad_param.grad					) is False
                     ), f'Gradients in sync when they should not be at iteration {iteration}:\nmodel_a grad ({param.grad}) == model_b grad ({grad_param.grad})'
              else:
                     # Grads should be in sync
                     assert (
                         torch.allclose(param.grad      ,							grad_param.grad					) is True
                     ), f'Gradients not in sync when they should be at iteration {iteration}:\nmodel_a grad ({param.grad}) != model_b grad ({grad_param.grad})'




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case=True					)  ->    str:
       model.train()
       lowercase__:       Any        =       model(snake_case					)
       lowercase__:       str        =       F.mse_loss(snake_case      ,							target.to(output.device					)					)
       if not do_backward:
              loss /= accelerator.gradient_accumulation_steps
              loss.backward()
       else:
              accelerator.backward(snake_case					)




def        snake_case_					(  snake_case      ,							snake_case=False					)  ->    int:
       set_seed(42					)
       lowercase__:       Optional[Any]        =       RegressionModel()
       lowercase__:       int        =       deepcopy(snake_case					)
       lowercase__:       str        =       RegressionDataset(length=80					)
       lowercase__:       Dict        =       DataLoader(snake_case      ,							batch_size=16					)
       model.to(accelerator.device					)
       if sched:
              lowercase__:       Union[str, Any]        =       AdamW(params=model.parameters()      ,							lr=1e-3					)
              lowercase__:       List[str]        =       AdamW(params=ddp_model.parameters()      ,							lr=1e-3					)
              lowercase__:       List[Any]        =       LambdaLR(snake_case      ,							lr_lambda=lambda snake_case					: epoch**0.6_5					)
              lowercase__:       Dict        =       LambdaLR(snake_case      ,							lr_lambda=lambda snake_case					: epoch**0.6_5					)
       # Make a copy of `model`
       if sched:
              lowercase__:       List[Any]        =       accelerator.prepare(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
       else:
              lowercase__:       Optional[int]        =       accelerator.prepare(snake_case      ,							snake_case					)
       if sched:
              return (model, opt, sched, dataloader, ddp_model, ddp_opt, ddp_sched)
       return model, ddp_model, dataloader




def        snake_case_					(  snake_case					)  ->    List[Any]:
       # Test when on a single CPU or GPU that the context manager does nothing
       lowercase__:       Optional[int]        =       get_training_setup(snake_case					)
       # Use a single batch
       lowercase__:       Dict        =       next(iter(snake_case					)					).values()
       for iteration in range(3					):
              # Gather the distributed inputs and targs for the base model
              lowercase__:       str        =       accelerator.gather((ddp_input, ddp_target)					)
              lowercase__:       Union[str, Any]        =       input.to(accelerator.device					), target.to(accelerator.device					)
              # Perform our initial ground truth step in non "DDP"
              step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              # Do "gradient accumulation" (noop)
              if iteration % 2 == 0:
                     # Accumulate grads locally
                     with accelerator.no_sync(snake_case					):
                            step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              else:
                     # Sync grads
                     step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)

              # Since `no_sync` is a noop, `ddp_model` and `model` grads should always be in sync
              check_model_parameters(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              for param, ddp_param in zip(model.parameters()      ,							ddp_model.parameters()					):
                     if not param.requires_grad:
                            continue
                     assert torch.allclose(
                         param.grad      ,							ddp_param.grad					), f'Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})'

              # Shuffle ddp_input on each iteration
              torch.manual_seed(13_37 + iteration					)
              lowercase__:       Optional[int]        =       ddp_input[torch.randperm(len(snake_case					)					)]




def        snake_case_					(  snake_case					)  ->    Optional[Any]:
       # Test on distributed setup that context manager behaves properly
       lowercase__:       int        =       get_training_setup(snake_case					)
       # Use a single batch
       lowercase__:       str        =       next(iter(snake_case					)					).values()
       for iteration in range(3					):
              # Gather the distributed inputs and targs for the base model
              lowercase__:       str        =       accelerator.gather((ddp_input, ddp_target)					)
              lowercase__:       Optional[int]        =       input.to(accelerator.device					), target.to(accelerator.device					)
              # Perform our initial ground truth step in non "DDP"
              step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              # Do "gradient accumulation" (noop)
              if iteration % 2 == 0:
                     # Accumulate grads locally
                     with accelerator.no_sync(snake_case					):
                            step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              else:
                     # Sync grads
                     step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)

              # DDP model and model should only be in sync when not (iteration % 2 == 0)
              for param, ddp_param in zip(model.parameters()      ,							ddp_model.parameters()					):
                     if not param.requires_grad:
                            continue
                     if iteration % 2 == 0:
                            # Grads should not be in sync
                            assert (
                                torch.allclose(param.grad      ,							ddp_param.grad					) is False
                            ), f'Gradients in sync when they should not be:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})'
                     else:
                            # Grads should be in sync
                            assert (
                                torch.allclose(param.grad      ,							ddp_param.grad					) is True
                            ), f'Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})'

        # Shuffle ddp_input on each iteration
              torch.manual_seed(13_37 + iteration					)
              lowercase__:       List[Any]        =       ddp_input[torch.randperm(len(snake_case					)					)]




def        snake_case_					(  snake_case=False      ,							snake_case=False					)  ->    List[str]:
       lowercase__:       List[str]        =       Accelerator(
           split_batches=snake_case      ,							dispatch_batches=snake_case      ,							gradient_accumulation_steps=2					)
       # Test that context manager behaves properly
       lowercase__:       List[str]        =       get_training_setup(snake_case					)
       for iteration, batch in enumerate(snake_case					):
              lowercase__:       Optional[Any]        =       batch.values()
              # Gather the distributed inputs and targs for the base model
              lowercase__:       Dict        =       accelerator.gather((ddp_input, ddp_target)					)
              lowercase__:       Optional[Any]        =       input.to(accelerator.device					), target.to(accelerator.device					)
              # Perform our initial ground truth step in non "DDP"
              step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              # Do "gradient accumulation" (noop)
              with accelerator.accumulate(snake_case					):
                     step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)

              # DDP model and model should only be in sync when not (iteration % 2 == 0)
              for param, ddp_param in zip(model.parameters()      ,							ddp_model.parameters()					):
                     if not param.requires_grad:
                            continue
                     if ((iteration + 1) % 2 == 0) or (iteration == len(snake_case					) - 1):
                            # Grads should be in sync
                            assert (
                                torch.allclose(param.grad      ,							ddp_param.grad					) is True
                            ), f'Gradients not in sync when they should be at iteration {iteration}:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})'
                     else:
                            # Grads should not be in sync
                            assert (
                                torch.allclose(param.grad      ,							ddp_param.grad					) is False
                            ), f'Gradients in sync when they should not be at iteration {iteration}:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})'

        # Shuffle ddp_input on each iteration
              torch.manual_seed(13_37 + iteration					)
              lowercase__:       str        =       ddp_input[torch.randperm(len(snake_case					)					)]
       GradientState._reset_state()




def        snake_case_					(  snake_case=False      ,							snake_case=False					)  ->    Dict:
       lowercase__:       Union[str, Any]        =       Accelerator(
           split_batches=snake_case      ,							dispatch_batches=snake_case      ,							gradient_accumulation_steps=2					)
       # Test that context manager behaves properly
       lowercase__:       Dict        =       get_training_setup(snake_case      ,							snake_case					)
       for iteration, batch in enumerate(snake_case					):
              lowercase__:       Optional[int]        =       batch.values()
              # Gather the distributed inputs and targs for the base model
              lowercase__:       str        =       accelerator.gather((ddp_input, ddp_target)					)
              lowercase__:       Optional[Any]        =       input.to(accelerator.device					), target.to(accelerator.device					)
              # Perform our initial ground truth step in non "DDP"
              model.train()
              ddp_model.train()
              step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              opt.step()

              if ((iteration + 1) % 2 == 0) or ((iteration + 1) == len(snake_case					)):
                     if split_batches:
                            sched.step()
                     else:
                            for _ in range(accelerator.num_processes					):
                                   sched.step()
              opt.zero_grad()
              # Perform gradient accumulation under wrapper
              with accelerator.accumulate(snake_case					):
                     step_model(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
                     ddp_opt.step()
                     ddp_sched.step()
                     ddp_opt.zero_grad()

              # Learning rates should be the same
              assert (
                  opt.param_groups[0]["lr"] == ddp_opt.param_groups[0]["lr"]
              ), f'Learning rates found in each optimizer did not align\nopt: {opt.param_groups[0]["lr"]}\nDDP opt: {ddp_opt.param_groups[0]["lr"]}\n'
              lowercase__:       Union[str, Any]        =       (((iteration + 1) % 2) == 0) or ((iteration + 1) == len(snake_case					))
              if accelerator.num_processes > 1:
                     check_model_parameters(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)
              # Shuffle ddp_input on each iteration
              torch.manual_seed(13_37 + iteration					)
       GradientState._reset_state()




def        snake_case_					(  )  ->    Optional[Any]:
       lowercase__:       Optional[int]        =       Accelerator()

       lowercase__:       Tuple        =       RegressionDataset(length=80					)
       lowercase__:       Any        =       DataLoader(snake_case      ,							batch_size=16					)
       lowercase__:       Union[str, Any]        =       RegressionDataset(length=96					)
       lowercase__:       Union[str, Any]        =       DataLoader(snake_case      ,							batch_size=16					)
       lowercase__:       List[str]        =       accelerator.prepare(snake_case      ,							snake_case					)
       assert accelerator.gradient_state.active_dataloader is None
       for iteration, _ in enumerate(snake_case					):
              assert id(accelerator.gradient_state.active_dataloader					) == id(snake_case					)
              if iteration < len(snake_case					) - 1:
                     assert not accelerator.gradient_state.end_of_dataloader
                     if iteration == 1:
                            for batch_num, _ in enumerate(snake_case					):
                                   assert id(accelerator.gradient_state.active_dataloader					) == id(snake_case					)
                                   if batch_num < len(snake_case					) - 1:
                                          assert not accelerator.gradient_state.end_of_dataloader
                                   else:
                                          assert accelerator.gradient_state.end_of_dataloader
              else:
                     assert accelerator.gradient_state.end_of_dataloader
       assert accelerator.gradient_state.active_dataloader is None




def        snake_case_					(  )  ->    int:
       lowercase__:       List[Any]        =       Accelerator()
       lowercase__:       Optional[int]        =       accelerator.state
       if state.local_process_index == 0:
              print('**Test `accumulate` gradient accumulation with dataloader break**'					)
       test_dataloader_break()
       if state.distributed_type == DistributedType.NO:
              if state.local_process_index == 0:
                     print('**Test NOOP `no_sync` context manager**'					)
              test_noop_sync(snake_case					)
       if state.distributed_type in (DistributedType.MULTI_GPU, DistributedType.MULTI_CPU):
              if state.local_process_index == 0:
                     print('**Test Distributed `no_sync` context manager**'					)
              test_distributed_sync(snake_case					)
       if state.distributed_type == DistributedType.MULTI_GPU:
              for split_batch in [True, False]:
                     for dispatch_batches in [True, False]:
                            if state.local_process_index == 0:
                                   print(
                                       '**Test `accumulate` gradient accumulation, '      ,							f'`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**'      ,							)
                            test_gradient_accumulation(snake_case      ,							snake_case					)

    # Currently will break on torch 2.0 +, need to investigate why
       if is_torch_version('<'      ,							'2.0'					) or state.distributed_type == DistributedType.NO:
              if state.local_process_index == 0:
                     print(
                         '**Test `accumulate` gradient accumulation with optimizer and scheduler, '      ,							'`split_batches=False`, `dispatch_batches=False`**'      ,							)
              test_gradient_accumulation_with_opt_and_scheduler()
              if state.distributed_type == DistributedType.MULTI_GPU:
                     for split_batch in [True, False]:
                            for dispatch_batches in [True, False]:
                                   if not split_batch and not dispatch_batches:
                                          continue
                                   if state.local_process_index == 0:
                                          print(
                                              '**Test `accumulate` gradient accumulation with optimizer and scheduler, '      ,							f'`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**'      ,							)
                                   test_gradient_accumulation_with_opt_and_scheduler(snake_case      ,							snake_case					)




def        snake_case_					(  snake_case					)  ->    int:
       # For xla_spawn (TPUs)
       main()


if __name__ == "__main__":
 main()



from math import pow




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							)  ->    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

       lowercase__:       int        =       int(pow(snake_case      ,							snake_case					)					)
       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
              lowercase__      ,						lowercase__:       Any        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
              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.
              lowercase__      ,						lowercase__:       Optional[int]        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
       return current_sum, solutions_count




def        snake_case_					(  snake_case      ,							snake_case					)  ->    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(snake_case      ,							snake_case      ,							1      ,							0      ,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()


