





def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      _enforce_args(__A			,      __A	)
      if n == 0:
            return 0
      _snake_case		:	List[str]					     =     float('''-inf'''	)
      for i in range(1			,      n + 1	):
            _snake_case		:	List[Any]					     =     max(
                __A			,      prices[i - 1] + naive_cut_rod_recursive(n - i			,      __A	)	)

      return max_revue




def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      _enforce_args(__A			,      __A	)
      _snake_case		:	Any					     =     [float('''-inf'''	) for _ in range(n + 1	)]
      return _top_down_cut_rod_recursive(__A			,      __A			,      __A	)




def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            _snake_case		:	Optional[int]					     =     float('''-inf'''	)
            for i in range(1			,      n + 1	):
                  _snake_case		:	List[str]					     =     max(
                      __A			,      prices[i - 1] + _top_down_cut_rod_recursive(n - i			,      __A			,      __A	)			,      )

            _snake_case		:	List[str]					     =     max_revenue

      return max_rev[n]




def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      _enforce_args(__A			,      __A	)

      # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
      # length 0.
      _snake_case		:	List[Any]					     =     [float('''-inf'''	) for _ in range(n + 1	)]
      _snake_case		:	Optional[int]					     =     0

      for i in range(1			,      n + 1	):
            _snake_case		:	int					     =     max_rev[i]
            for j in range(1			,      i + 1	):
                  _snake_case		:	Union[str, Any]					     =     max(__A			,      prices[j - 1] + max_rev[i - j]	)

            _snake_case		:	Union[str, Any]					     =     max_revenue_i

      return max_rev[n]




def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      if n < 0:
            _snake_case		:	List[str]					     =     f'''n must be greater than or equal to 0. Got n = {n}'''
            raise ValueError(__A	)

      if n > len(__A	):
            _snake_case		:	List[Any]					     =     (
                '''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"""



      _snake_case		:	str					     =     [6, 10, 12, 15, 20, 23]
      _snake_case		:	Optional[Any]					     =     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.
      _snake_case		:	int					     =     36

      _snake_case		:	str					     =     top_down_cut_rod(__A			,      __A	)
      _snake_case		:	int					     =     bottom_up_cut_rod(__A			,      __A	)
      _snake_case		:	str					     =     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()









'''simple docstring'''

import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu





@require_cpu
class lowerCamelCase						(unittest.TestCase					):







  def 				UpperCAmelCase_				(		self		)		->						Union[str, Any]:






        """simple docstring"""





        _snake_case		:	Any					     =     torch.nn.Linear(10     ,     10		)
        _snake_case		:	Optional[int]					     =     torch.optim.SGD(model.parameters()     ,     0.1		)
        _snake_case		:	List[str]					     =     Accelerator()
        _snake_case		:	Optional[Any]					     =     accelerator.prepare(lowercase__		)
        try:
              pickle.loads(pickle.dumps(lowercase__		)		)
        except Exception as e:
              self.fail(F'''Accelerated optimizer pickling failed with {e}'''		)
        AcceleratorState._reset_state()


