
"""simple docstring"""



# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)





@flax.struct.dataclass
class 				a			:
      UpperCamelCase							:   CommonSchedulerState

      # setable values
      UpperCamelCase							:   jnp.ndarray
      UpperCamelCase							:   jnp.ndarray
      UpperCamelCase							:   Optional[int]           =     None



      @classmethod
      def  __snake_case							(   cls     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_      ):
          return cls(common=UpperCamelCase_     ,	init_noise_sigma=UpperCamelCase_     ,	timesteps=UpperCamelCase_      )





@dataclass
class 				a			(					lowercase      ):
      UpperCamelCase							:   DDPMSchedulerState





class 				a			(					lowercase						,		lowercase      ):
      UpperCamelCase							:   List[str]           =     [e.name for e in FlaxKarrasDiffusionSchedulers]

      UpperCamelCase							:   jnp.dtype



      @property
      def  __snake_case							(   self      ):
          return True



      @register_to_config
      def __init__(   self     ,	UpperCamelCase_ = 1_000     ,	UpperCamelCase_ = 0.0001     ,	UpperCamelCase_ = 0.02     ,	UpperCamelCase_ = "linear"     ,	UpperCamelCase_ = None     ,	UpperCamelCase_ = "fixed_small"     ,	UpperCamelCase_ = True     ,	UpperCamelCase_ = "epsilon"     ,	UpperCamelCase_ = jnp.floataa     ,	):
          UpperCAmelCase__	:      Any     							=					dtype



      def  __snake_case							(   self     ,	UpperCamelCase_ = None      ):
          if common is None:
              UpperCAmelCase__	:      Dict     							=					CommonSchedulerState.create(self      )

          # standard deviation of the initial noise distribution
          UpperCAmelCase__	:      Union[str, Any]     							=					jnp.array(1.0     ,	dtype=self.dtype      )

          UpperCAmelCase__	:      int     							=					jnp.arange(0     ,	self.config.num_train_timesteps      ).round()[::-1]

          return DDPMSchedulerState.create(
              common=UpperCamelCase_     ,	init_noise_sigma=UpperCamelCase_     ,	timesteps=UpperCamelCase_     ,	)



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_ = None      ):
          return sample



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_ = ()      ):
          UpperCAmelCase__	:      Optional[int]     							=					self.config.num_train_timesteps // num_inference_steps
          # creates integer timesteps by multiplying by ratio
          # rounding to avoid issues when num_inference_step is power of 3
          UpperCAmelCase__	:      int     							=					(jnp.arange(0     ,	UpperCamelCase_      ) * step_ratio).round()[::-1]

          return state.replace(
              num_inference_steps=UpperCamelCase_     ,	timesteps=UpperCamelCase_     ,	)



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_=None     ,	UpperCamelCase_=None      ):
          UpperCAmelCase__	:      Optional[int]     							=					state.common.alphas_cumprod[t]
          UpperCAmelCase__	:      str     							=					jnp.where(t > 0     ,	state.common.alphas_cumprod[t - 1]     ,	jnp.array(1.0     ,	dtype=self.dtype      )      )

          # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
          # and sample from it to get previous sample
          # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
          UpperCAmelCase__	:      Optional[int]     							=					(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

          if variance_type is None:
              UpperCAmelCase__	:      List[Any]     							=					self.config.variance_type

          # hacks - were probably added for training stability
          if variance_type == "fixed_small":
              UpperCAmelCase__	:      Optional[int]     							=					jnp.clip(UpperCamelCase_     ,	a_min=1E-20      )
          # for rl-diffuser https://arxiv.org/abs/2205.09991
          elif variance_type == "fixed_small_log":
              UpperCAmelCase__	:      List[Any]     							=					jnp.log(jnp.clip(UpperCamelCase_     ,	a_min=1E-20      )      )
          elif variance_type == "fixed_large":
              UpperCAmelCase__	:      Any     							=					state.common.betas[t]
          elif variance_type == "fixed_large_log":
              # Glide max_log
              UpperCAmelCase__	:      Tuple     							=					jnp.log(state.common.betas[t]      )
          elif variance_type == "learned":
              return predicted_variance
          elif variance_type == "learned_range":
              UpperCAmelCase__	:      Any     							=					variance
              UpperCAmelCase__	:      Any     							=					state.common.betas[t]
              UpperCAmelCase__	:      Tuple     							=					(predicted_variance + 1) / 2
              UpperCAmelCase__	:      Any     							=					frac * max_log + (1 - frac) * min_log

          return variance



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_ = None     ,	UpperCamelCase_ = True     ,	):
          UpperCAmelCase__	:      int     							=					timestep

          if key is None:
              UpperCAmelCase__	:      Optional[int]     							=					jax.random.PRNGKey(0      )

          if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
              UpperCAmelCase__							,							UpperCAmelCase__	:      List[Any]     							=					jnp.split(UpperCamelCase_     ,	sample.shape[1]     ,	axis=1      )
          else:
              UpperCAmelCase__	:      str     							=					None

          # 1. compute alphas, betas
          UpperCAmelCase__	:      str     							=					state.common.alphas_cumprod[t]
          UpperCAmelCase__	:      Optional[Any]     							=					jnp.where(t > 0     ,	state.common.alphas_cumprod[t - 1]     ,	jnp.array(1.0     ,	dtype=self.dtype      )      )
          UpperCAmelCase__	:      Optional[Any]     							=					1 - alpha_prod_t
          UpperCAmelCase__	:      Any     							=					1 - alpha_prod_t_prev

          # 2. compute predicted original sample from predicted noise also called
          # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
          if self.config.prediction_type == "epsilon":
              UpperCAmelCase__	:      List[str]     							=					(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
          elif self.config.prediction_type == "sample":
              UpperCAmelCase__	:      Optional[int]     							=					model_output
          elif self.config.prediction_type == "v_prediction":
              UpperCAmelCase__	:      Optional[int]     							=					(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
          else:
              raise ValueError(
                  F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` '''
                  ' for the FlaxDDPMScheduler.'      )

          # 3. Clip "predicted x_0"
          if self.config.clip_sample:
              UpperCAmelCase__	:      Tuple     							=					jnp.clip(UpperCamelCase_     ,	-1     ,	1      )

          # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
          # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
          UpperCAmelCase__	:      List[Any]     							=					(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
          UpperCAmelCase__	:      Tuple     							=					state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

          # 5. Compute predicted previous sample µ_t
          # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
          UpperCAmelCase__	:      List[str]     							=					pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

          # 6. Add noise
          def random_variance():
              UpperCAmelCase__	:      Union[str, Any]     							=					jax.random.split(UpperCamelCase_     ,	num=1      )
              UpperCAmelCase__	:      Any     							=					jax.random.normal(UpperCamelCase_     ,	shape=model_output.shape     ,	dtype=self.dtype      )
              return (self._get_variance(UpperCamelCase_     ,	UpperCamelCase_     ,	predicted_variance=UpperCamelCase_      ) ** 0.5) * noise

          UpperCAmelCase__	:      str     							=					jnp.where(t > 0     ,	random_variance()     ,	jnp.zeros(model_output.shape     ,	dtype=self.dtype      )      )

          UpperCAmelCase__	:      Optional[Any]     							=					pred_prev_sample + variance

          if not return_dict:
              return (pred_prev_sample, state)

          return FlaxDDPMSchedulerOutput(prev_sample=UpperCamelCase_     ,	state=UpperCamelCase_      )



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	):
          return add_noise_common(state.common     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_      )



      def  __snake_case							(   self     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	):
          return get_velocity_common(state.common     ,	UpperCamelCase_     ,	UpperCamelCase_     ,	UpperCamelCase_      )



      def __len__(   self      ):
          return self.config.num_train_timesteps



"""simple docstring"""



def 					lowerCamelCase   (     _snake_case    ,_snake_case    ,_snake_case ):
    if len(_snake_case ) != len(_snake_case ):
        raise ValueError('The length of profit and weight must be same.' )
    if max_weight <= 0:
        raise ValueError('max_weight must greater than zero.' )
    if any(p < 0 for p in profit ):
        raise ValueError('Profit can not be negative.' )
    if any(w < 0 for w in weight ):
        raise ValueError('Weight can not be negative.' )

    # List created to store profit gained for the 1kg in case of each weight
    # respectively.  Calculate and append profit/weight for each element.
    UpperCAmelCase__	:      Any     							=					[p / w for p, w in zip(_snake_case    ,_snake_case )]

    # Creating a copy of the list and sorting profit/weight in ascending order
    UpperCAmelCase__	:      Union[str, Any]     							=					sorted(_snake_case )

    # declaring useful variables
    UpperCAmelCase__	:      Tuple     							=					len(_snake_case )
    UpperCAmelCase__	:      List[Any]     							=					0
    UpperCAmelCase__	:      Union[str, Any]     							=					0
    UpperCAmelCase__	:      Any     							=					0

    # loop till the total weight do not reach max limit e.g. 15 kg and till i<length
    while limit <= max_weight and i < length:
        # flag value for encountered greatest element in sorted_profit_by_weight
        UpperCAmelCase__	:      Tuple     							=					sorted_profit_by_weight[length - i - 1]
        UpperCAmelCase__	:      int     							=					profit_by_weight.index(_snake_case )
        UpperCAmelCase__	:      str     							=					-1

        # check if the weight encountered is less than the total weight
        # encountered before.
        if max_weight - limit >= weight[index]:
            limit += weight[index]
            # Adding profit gained for the given weight 1 ===
            # weight[index]/weight[index]
            gain += 1 * profit[index]
        else:
            # Since the weight encountered is greater than limit, therefore take the
            # required number of remaining kgs and calculate profit for it.
            # weight remaining / weight[index]
            gain += (max_weight - limit) / weight[index] * profit[index]
            break
        i += 1
    return gain


if __name__ == "__main__":
    print(
        'Input profits, weights, and then max_weight (all positive ints) separated by '
        'spaces.'
    )

    UpperCamelCase__          =	[int(x) for x in input('Input profits separated by spaces: ').split()]
    UpperCamelCase__          =	[int(x) for x in input('Input weights separated by spaces: ').split()]
    UpperCamelCase__          =	int(input('Max weight allowed: '))

    # Function Call
    calc_profit(profit, weight, max_weight)

