





"""simple docstring"""




def 					_A	(		SCREAMING_SNAKE_CASE					:       List[Any]	,	SCREAMING_SNAKE_CASE					:       Optional[int]	,	SCREAMING_SNAKE_CASE					:       str	,	SCREAMING_SNAKE_CASE					:       Optional[Any]						):





  """simple docstring"""



  global f  # a global dp table for knapsack
  if f[i][j] < 0:
    if j < wt[i - 1]:
      a__     : Dict  =mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
    else:
      a__     : str  =max(
          mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)	,	mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	j - wt[i - 1]						) + val[i - 1]	,	)
    a__     : Optional[Any]  =val
  return f[i][j]
def 					_A	(		SCREAMING_SNAKE_CASE					:       Dict	,	SCREAMING_SNAKE_CASE					:       Dict	,	SCREAMING_SNAKE_CASE					:       List[str]	,	SCREAMING_SNAKE_CASE					:       Dict						):





  """simple docstring"""



  a__     : Tuple  =[[0] * (w + 1) for _ in range(n + 1						)]

  for i in range(1	,	n + 1						):
    for w_ in range(1	,	w + 1						):
      if wt[i - 1] <= w_:
        a__     : Optional[Any]  =max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]	,	dp[i - 1][w_]						)
      else:
        a__     : str  =dp[i - 1][w_]

  return dp[n][w_], dp
def 					_A	(		SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       list						):





  """simple docstring"""



  if not (isinstance(SCREAMING_SNAKE_CASE	,	(list, tuple)						) and isinstance(SCREAMING_SNAKE_CASE	,	(list, tuple)						)):
    raise ValueError(
        "Both the weights and values vectors must be either lists or tuples"						)

  a__     : Any  =len(SCREAMING_SNAKE_CASE						)
  if num_items != len(SCREAMING_SNAKE_CASE						):
    a__     : Dict  =(
        "The number of weights must be the same as the number of values.\n"
        f'''But got {num_items} weights and {len(SCREAMING_SNAKE_CASE						)} values'''
    )
    raise ValueError(SCREAMING_SNAKE_CASE						)
  for i in range(SCREAMING_SNAKE_CASE						):
    if not isinstance(wt[i]	,	SCREAMING_SNAKE_CASE						):
      a__     : Optional[Any]  =(
          "All weights must be integers but got weight of "
          f'''type {type(wt[i]						)} at index {i}'''
      )
      raise TypeError(SCREAMING_SNAKE_CASE						)

  a__     : Any  =knapsack(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
  a__     : set  =set()
  _construct_solution(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)

  return optimal_val, example_optional_set
def 					_A	(		SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       set						):





  """simple docstring"""



  if i > 0 and j > 0:
    if dp[i - 1][j] == dp[i][j]:
      _construct_solution(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
    else:
      optimal_set.add(SCREAMING_SNAKE_CASE						)
      _construct_solution(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	i - 1	,	j - wt[i - 1]	,	SCREAMING_SNAKE_CASE						)


if __name__ == "__main__":
     UpperCAmelCase     :     Dict							=	[3, 2, 4, 4]
     UpperCAmelCase     :     Tuple							=	[4, 3, 2, 3]
     UpperCAmelCase     :     str							=	4
     UpperCAmelCase     :     Tuple							=	6
     UpperCAmelCase     :     Tuple							=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
     UpperCAmelCase     :     List[Any]							=	knapsack(w, wt, val, n)
     print(optimal_solution)
     print(mf_knapsack(n, wt, val, w))  # switched the n and w

     # testing the dynamic programming problem with example
     # the optimal subset for the above example are items 3 and 4
     UpperCAmelCase     :     Union[str, Any]							=	knapsack_with_example_solution(w, wt, val)
     assert optimal_solution == 8
     assert optimal_subset == {3, 4}
     print("""optimal_value = """, optimal_solution)
     print("""An optimal subset corresponding to the optimal value""", optimal_subset)













import tempfile

import torch

from diffusers import PNDMScheduler

from .test_schedulers import SchedulerCommonTest







class     __lowerCAmelCase	(   UpperCamelCase__):
      _lowercase    : Any            =      (PNDMScheduler,)
      _lowercase    : str            =      (("""num_inference_steps""", 50),)







      def        _lowercase  (   self		,				**lowerCAmelCase__							)       ->						int:



        '''simple docstring'''




        a__     : Dict  ={
            "num_train_timesteps": 1_0_0_0,
            "beta_start": 0.00_01,
            "beta_end": 0.02,
            "beta_schedule": "linear",
        }

        config.update(**lowerCAmelCase__							)
        return config







      def        _lowercase  (   self		,				lowerCAmelCase__=0		,				**lowerCAmelCase__							)       ->						List[Any]:



        '''simple docstring'''




        a__     : Optional[int]  =dict(self.forward_default_kwargs							)
        a__     : Tuple  =kwargs.pop("num_inference_steps"		,				lowerCAmelCase__							)
        a__     : List[str]  =self.dummy_sample
        a__     : List[str]  =0.1 * sample
        a__     : str  =[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

        for scheduler_class in self.scheduler_classes:
          a__     : int  =self.get_scheduler_config(**lowerCAmelCase__							)
          a__     : Union[str, Any]  =scheduler_class(**lowerCAmelCase__							)
          scheduler.set_timesteps(lowerCAmelCase__							)
          # copy over dummy past residuals
          a__     : Any  =dummy_past_residuals[:]

          with tempfile.TemporaryDirectory() as tmpdirname:
            scheduler.save_config(lowerCAmelCase__							)
            a__     : List[Any]  =scheduler_class.from_pretrained(lowerCAmelCase__							)
            new_scheduler.set_timesteps(lowerCAmelCase__							)
            # copy over dummy past residuals
            a__     : str  =dummy_past_residuals[:]

          a__     : Any  =scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : Dict  =new_scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          assert torch.sum(torch.abs(output - new_output							)							) < 1E-5, "Scheduler outputs are not identical"

          a__     : Optional[int]  =scheduler.step_plms(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : Union[str, Any]  =new_scheduler.step_plms(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          assert torch.sum(torch.abs(output - new_output							)							) < 1E-5, "Scheduler outputs are not identical"







      def        _lowercase  (   self							)       ->						int:



        '''simple docstring'''




        pass







      def        _lowercase  (   self		,				lowerCAmelCase__=0		,				**lowerCAmelCase__							)       ->						Optional[Any]:



        '''simple docstring'''




        a__     : Optional[int]  =dict(self.forward_default_kwargs							)
        a__     : List[str]  =kwargs.pop("num_inference_steps"		,				lowerCAmelCase__							)
        a__     : List[str]  =self.dummy_sample
        a__     : int  =0.1 * sample
        a__     : Tuple  =[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

        for scheduler_class in self.scheduler_classes:
          a__     : Dict  =self.get_scheduler_config()
          a__     : List[str]  =scheduler_class(**lowerCAmelCase__							)
          scheduler.set_timesteps(lowerCAmelCase__							)

          # copy over dummy past residuals (must be after setting timesteps)
          a__     : Dict  =dummy_past_residuals[:]

          with tempfile.TemporaryDirectory() as tmpdirname:
            scheduler.save_config(lowerCAmelCase__							)
            a__     : Dict  =scheduler_class.from_pretrained(lowerCAmelCase__							)
            # copy over dummy past residuals
            new_scheduler.set_timesteps(lowerCAmelCase__							)

            # copy over dummy past residual (must be after setting timesteps)
            a__     : Optional[int]  =dummy_past_residuals[:]

          a__     : Optional[Any]  =scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : List[Any]  =new_scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          assert torch.sum(torch.abs(output - new_output							)							) < 1E-5, "Scheduler outputs are not identical"

          a__     : List[str]  =scheduler.step_plms(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : Any  =new_scheduler.step_plms(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          assert torch.sum(torch.abs(output - new_output							)							) < 1E-5, "Scheduler outputs are not identical"







      def        _lowercase  (   self		,				**lowerCAmelCase__							)       ->						int:



        '''simple docstring'''




        a__     : Union[str, Any]  =self.scheduler_classes[0]
        a__     : Optional[Any]  =self.get_scheduler_config(**lowerCAmelCase__							)
        a__     : Any  =scheduler_class(**lowerCAmelCase__							)

        a__     : int  =1_0
        a__     : Union[str, Any]  =self.dummy_model()
        a__     : Optional[int]  =self.dummy_sample_deter
        scheduler.set_timesteps(lowerCAmelCase__							)

        for i, t in enumerate(scheduler.prk_timesteps							):
          a__     : List[Any]  =model(lowerCAmelCase__		,				lowerCAmelCase__							)
          a__     : Optional[Any]  =scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__							).prev_sample

        for i, t in enumerate(scheduler.plms_timesteps							):
          a__     : int  =model(lowerCAmelCase__		,				lowerCAmelCase__							)
          a__     : int  =scheduler.step_plms(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__							).prev_sample

        return sample







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



        '''simple docstring'''




        a__     : str  =dict(self.forward_default_kwargs							)

        a__     : Tuple  =kwargs.pop("num_inference_steps"		,				lowerCAmelCase__							)

        for scheduler_class in self.scheduler_classes:
          a__     : Union[str, Any]  =self.get_scheduler_config()
          a__     : List[str]  =scheduler_class(**lowerCAmelCase__							)

          a__     : List[Any]  =self.dummy_sample
          a__     : Dict  =0.1 * sample

          if num_inference_steps is not None and hasattr(lowerCAmelCase__		,				"set_timesteps"							):
            scheduler.set_timesteps(lowerCAmelCase__							)
          elif num_inference_steps is not None and not hasattr(lowerCAmelCase__		,				"set_timesteps"							):
            a__     : int  =num_inference_steps

          # copy over dummy past residuals (must be done after set_timesteps)
          a__     : Tuple  =[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]
          a__     : str  =dummy_past_residuals[:]

          a__     : List[Any]  =scheduler.step_prk(lowerCAmelCase__		,				0		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : int  =scheduler.step_prk(lowerCAmelCase__		,				1		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          self.assertEqual(output_a.shape		,				sample.shape							)
          self.assertEqual(output_a.shape		,				output_a.shape							)

          a__     : List[str]  =scheduler.step_plms(lowerCAmelCase__		,				0		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample
          a__     : Dict  =scheduler.step_plms(lowerCAmelCase__		,				1		,				lowerCAmelCase__		,				**lowerCAmelCase__							).prev_sample

          self.assertEqual(output_a.shape		,				sample.shape							)
          self.assertEqual(output_a.shape		,				output_a.shape							)







      def        _lowercase  (   self							)       ->						Tuple:



        '''simple docstring'''




        for timesteps in [1_0_0, 1_0_0_0]:
          self.check_over_configs(num_train_timesteps=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						Optional[Any]:



        '''simple docstring'''




        for steps_offset in [0, 1]:
          self.check_over_configs(steps_offset=lowerCAmelCase__							)

        a__     : Optional[Any]  =self.scheduler_classes[0]
        a__     : Tuple  =self.get_scheduler_config(steps_offset=1							)
        a__     : Optional[Any]  =scheduler_class(**lowerCAmelCase__							)
        scheduler.set_timesteps(1_0							)
        assert torch.equal(
            scheduler.timesteps		,				torch.LongTensor(
                [9_0_1, 8_5_1, 8_5_1, 8_0_1, 8_0_1, 7_5_1, 7_5_1, 7_0_1, 7_0_1, 6_5_1, 6_5_1, 6_0_1, 6_0_1, 5_0_1, 4_0_1, 3_0_1, 2_0_1, 1_0_1, 1]							)		,				)







      def        _lowercase  (   self							)       ->						Tuple:



        '''simple docstring'''




        for beta_start, beta_end in zip([0.00_01, 0.0_01]		,				[0.0_02, 0.02]							):
          self.check_over_configs(beta_start=lowerCAmelCase__		,				beta_end=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						List[str]:



        '''simple docstring'''




        for schedule in ["linear", "squaredcos_cap_v2"]:
          self.check_over_configs(beta_schedule=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						List[str]:



        '''simple docstring'''




        for prediction_type in ["epsilon", "v_prediction"]:
          self.check_over_configs(prediction_type=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						Dict:



        '''simple docstring'''




        for t in [1, 5, 1_0]:
          self.check_over_forward(time_step=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						List[Any]:



        '''simple docstring'''




        for t, num_inference_steps in zip([1, 5, 1_0]		,				[1_0, 5_0, 1_0_0]							):
          self.check_over_forward(num_inference_steps=lowerCAmelCase__							)







      def        _lowercase  (   self							)       ->						str:



        '''simple docstring'''




        a__     : Dict  =2_7

        for scheduler_class in self.scheduler_classes:
          a__     : Tuple  =self.dummy_sample
          a__     : Dict  =0.1 * sample

          a__     : Dict  =self.get_scheduler_config()
          a__     : int  =scheduler_class(**lowerCAmelCase__							)

          scheduler.set_timesteps(lowerCAmelCase__							)

          # before power of 3 fix, would error on first step, so we only need to do two
          for i, t in enumerate(scheduler.prk_timesteps[:2]							):
            a__     : Any  =scheduler.step_prk(lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__							).prev_sample







      def        _lowercase  (   self							)       ->						Optional[Any]:



        '''simple docstring'''




        with self.assertRaises(lowerCAmelCase__							):
          a__     : List[Any]  =self.scheduler_classes[0]
          a__     : Dict  =self.get_scheduler_config()
          a__     : Tuple  =scheduler_class(**lowerCAmelCase__							)

          scheduler.step_plms(self.dummy_sample		,				1		,				self.dummy_sample							).prev_sample







      def        _lowercase  (   self							)       ->						Optional[Any]:



        '''simple docstring'''




        a__     : List[Any]  =self.full_loop()
        a__     : str  =torch.sum(torch.abs(lowerCAmelCase__							)							)
        a__     : Optional[Any]  =torch.mean(torch.abs(lowerCAmelCase__							)							)

        assert abs(result_sum.item() - 1_98.13_18							) < 1E-2
        assert abs(result_mean.item() - 0.25_80							) < 1E-3







      def        _lowercase  (   self							)       ->						str:



        '''simple docstring'''




        a__     : str  =self.full_loop(prediction_type="v_prediction"							)
        a__     : int  =torch.sum(torch.abs(lowerCAmelCase__							)							)
        a__     : Optional[int]  =torch.mean(torch.abs(lowerCAmelCase__							)							)

        assert abs(result_sum.item() - 67.39_86							) < 1E-2
        assert abs(result_mean.item() - 0.08_78							) < 1E-3







      def        _lowercase  (   self							)       ->						Optional[int]:



        '''simple docstring'''




        a__     : Tuple  =self.full_loop(set_alpha_to_one=lowerCAmelCase__		,				beta_start=0.01							)
        a__     : str  =torch.sum(torch.abs(lowerCAmelCase__							)							)
        a__     : Dict  =torch.mean(torch.abs(lowerCAmelCase__							)							)

        assert abs(result_sum.item() - 2_30.03_99							) < 1E-2
        assert abs(result_mean.item() - 0.29_95							) < 1E-3







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



        '''simple docstring'''




        a__     : Dict  =self.full_loop(set_alpha_to_one=lowerCAmelCase__		,				beta_start=0.01							)
        a__     : Union[str, Any]  =torch.sum(torch.abs(lowerCAmelCase__							)							)
        a__     : Union[str, Any]  =torch.mean(torch.abs(lowerCAmelCase__							)							)

        assert abs(result_sum.item() - 1_86.94_82							) < 1E-2
        assert abs(result_mean.item() - 0.24_34							) < 1E-3






