"""simple docstring"""



import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class 				snake_case__     (   snake_case_   ):
 _snake_case   :			torch.FloatTensor
 _snake_case   :			Optional[torch.FloatTensor]           =		None



def 					_lowerCamelCase(					a ,  a=0.9_99 ,  a="cosine" ,  ):
       if alpha_transform_type == "cosine":

              def alpha_bar_fn(a							):
                     return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2							) ** 2

       elif alpha_transform_type == "exp":

              def alpha_bar_fn(a							):
                     return math.exp(t * -12.0							)

       else:
              raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"							)

       __a     				=  []
       for i in range(a							):
              __a     				=  i / num_diffusion_timesteps
              __a     				=  (i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar_fn(a							) / alpha_bar_fn(a							) ,  a							)							)
       return torch.tensor(a ,  dtype=torch.floataa							)






class 				snake_case__     (   snake_case_,		snake_case_   ):
 _snake_case   :			str           =		1


 @register_to_config
 def __init__(				self  ,						lowerCamelCase = 1000  ,						lowerCamelCase = 0.0001  ,						lowerCamelCase = 0.02  ,						lowerCamelCase = "linear"  ,						lowerCamelCase = None  ,						lowerCamelCase = True  ,						lowerCamelCase = True  ,						lowerCamelCase = 0  ,						lowerCamelCase = "epsilon"  ,						lowerCamelCase = 1.0  ,						**lowerCamelCase  ,						):
        if kwargs.get("set_alpha_to_one"  ,						lowerCamelCase		) is not None:
               __a     				=  (
                   "The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."
               )
               deprecate("set_alpha_to_one"  ,						"1.0.0"  ,						lowerCamelCase  ,						standard_warn=lowerCamelCase		)
               __a     				=  kwargs["set_alpha_to_one"]
        if trained_betas is not None:
               __a     				=  torch.tensor(lowerCamelCase  ,						dtype=torch.floataa		)
        elif beta_schedule == "linear":
               __a     				=  torch.linspace(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						dtype=torch.floataa		)
        elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               __a     				=  (
                   torch.linspace(beta_start**0.5  ,						beta_end**0.5  ,						lowerCamelCase  ,						dtype=torch.floataa		) ** 2
               )
        elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               __a     				=  betas_for_alpha_bar(lowerCamelCase		)
        else:
               raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"		)

        __a     				=  1.0 - self.betas
        __a     				=  torch.cumprod(self.alphas  ,						dim=0		)

        # At every step in inverted ddim, we are looking into the next alphas_cumprod
        # For the final step, there is no next alphas_cumprod, and the index is out of bounds
        # `set_alpha_to_zero` decides whether we set this parameter simply to zero
        # in this case, self.step() just output the predicted noise
        # or whether we use the final alpha of the "non-previous" one.
        __a     				=  torch.tensor(0.0		) if set_alpha_to_zero else self.alphas_cumprod[-1]

        # standard deviation of the initial noise distribution
        __a     				=  1.0

        # setable values
        __a     				=  None
        __a     				=  torch.from_numpy(np.arange(0  ,						lowerCamelCase		).copy().astype(np.intaa		)		)


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase = None		):
        return sample


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase = None		):

        if num_inference_steps > self.config.num_train_timesteps:
               raise ValueError(
                   F"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
                   F" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
                   F" maximal {self.config.num_train_timesteps} timesteps."		)

        __a     				=  num_inference_steps
        __a     				=  self.config.num_train_timesteps // self.num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # casting to int to avoid issues when num_inference_step is power of 3
        __a     				=  (np.arange(0  ,						lowerCamelCase		) * step_ratio).round().copy().astype(np.intaa		)
        __a     				=  torch.from_numpy(lowerCamelCase		).to(lowerCamelCase		)
        self.timesteps += self.config.steps_offset


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase = 0.0  ,						lowerCamelCase = False  ,						lowerCamelCase = None  ,						lowerCamelCase = True  ,						):
        # 1. get previous step value (=t+1)
        __a     				=  timestep + self.config.num_train_timesteps // self.num_inference_steps

        # 2. compute alphas, betas
        # change original implementation to exactly match noise levels for analogous forward process
        __a     				=  self.alphas_cumprod[timestep]
        __a     				=  (
            self.alphas_cumprod[prev_timestep]
            if prev_timestep < self.config.num_train_timesteps
            else self.final_alpha_cumprod
        )

        __a     				=  1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        if self.config.prediction_type == "epsilon":
               __a     				=  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
               __a     				=  model_output
        elif self.config.prediction_type == "sample":
               __a     				=  model_output
               __a     				=  (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
        elif self.config.prediction_type == "v_prediction":
               __a     				=  (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
               __a     				=  (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
        else:
               raise ValueError(
                   F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                   " `v_prediction`"		)

        # 4. Clip or threshold "predicted x_0"
        if self.config.clip_sample:
               __a     				=  pred_original_sample.clamp(
                   -self.config.clip_sample_range  ,						self.config.clip_sample_range		)

        # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        __a     				=  (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

        # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        __a     				=  alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

        if not return_dict:
               return (prev_sample, pred_original_sample)
        return DDIMSchedulerOutput(prev_sample=lowerCamelCase  ,						pred_original_sample=lowerCamelCase		)






 def __len__(				self		):
        return self.config.num_train_timesteps
"""simple docstring"""



def 					_lowerCamelCase(					a ,  a ,  a ,  a							):
       global f  # a global dp table for knapsack
       if f[i][j] < 0:
              if j < wt[i - 1]:
                     __a     				=  mf_knapsack(i - 1 ,  a ,  a ,  a							)
              else:
                     __a     				=  max(
                         mf_knapsack(i - 1 ,  a ,  a ,  a							) ,  mf_knapsack(i - 1 ,  a ,  a ,  j - wt[i - 1]							) + val[i - 1] ,  )
              __a     				=  val
       return f[i][j]



def 					_lowerCamelCase(					a ,  a ,  a ,  a							):
       __a     				=  [[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     				=  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]] ,  dp[i - 1][w_]							)
                     else:
                            __a     				=  dp[i - 1][w_]

       return dp[n][w_], dp



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

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

       __a				, __a     				=  knapsack(a ,  a ,  a ,  a							)
       __a     				=  set()
       _construct_solution(a ,  a ,  a ,  a ,  a							)

       return optimal_val, example_optional_set



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a							):
       # for the current item i at a maximum weight j to be part of an optimal subset,
       # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
       # where i - 1 means considering only the previous items at the given maximum weight
       if i > 0 and j > 0:
              if dp[i - 1][j] == dp[i][j]:
                     _construct_solution(a ,  a ,  i - 1 ,  a ,  a							)
              else:
                     optimal_set.add(a							)
                     _construct_solution(a ,  a ,  i - 1 ,  j - wt[i - 1] ,  a							)


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE__:Tuple			=	[3, 2, 4, 4]
   SCREAMING_SNAKE_CASE__:List[str]			=	[4, 3, 2, 3]
   SCREAMING_SNAKE_CASE__:List[str]			=	4
   SCREAMING_SNAKE_CASE__:List[str]			=	6
   SCREAMING_SNAKE_CASE__:Optional[Any]			=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[int]			=	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
   SCREAMING_SNAKE_CASE__	,      SCREAMING_SNAKE_CASE__:Optional[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)
