



'''simple docstring'''
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class        __SCREAMING_SNAKE_CASE (     lowerCamelCase			):
 snake_case_												=							42
 snake_case_												=							None





def 	_a(					UpperCamelCase__			:  List[str],		UpperCamelCase__			:  Optional[Any]=0.9_9_9,		UpperCamelCase__			:  List[Any]="cosine",		):




      '''simple docstring'''






      if alpha_transform_type == "cosine":

            def alpha_bar_fn(UpperCamelCase__			:  Optional[Any]							):
                  return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2							) ** 2

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(UpperCamelCase__			:  List[str]							):
                  return math.exp(t * -1_2.0							)

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

      SCREAMING_SNAKE_CASE__       :			str													=[]
      for i in range(UpperCamelCase__							):
            SCREAMING_SNAKE_CASE__       :			int													=i / num_diffusion_timesteps
            SCREAMING_SNAKE_CASE__       :			Optional[Any]													=(i + 1) / num_diffusion_timesteps
            betas.append(min(1 - alpha_bar_fn(UpperCamelCase__							) / alpha_bar_fn(UpperCamelCase__							),		UpperCamelCase__							)							)
      return torch.tensor(UpperCamelCase__,		dtype=torch.floataa							)







class        __SCREAMING_SNAKE_CASE (     lowerCamelCase		,			lowerCamelCase			):




 @register_to_config
 def __init__( self		:							str   , __lowercase		:							int = 10_00   , __lowercase		:							str = "fixed_small_log"   , __lowercase		:							bool = True   , __lowercase		:							Optional[float] = 1.0   , __lowercase		:							str = "epsilon"   , __lowercase		:							str = "squaredcos_cap_v2"   , )		->  Dict:
       if beta_schedule != "squaredcos_cap_v2":
             raise ValueError('''UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'''' )

       SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=betas_for_alpha_bar(__lowercase )

       SCREAMING_SNAKE_CASE__       :			Optional[int]													=1.0 - self.betas
       SCREAMING_SNAKE_CASE__       :			Tuple													=torch.cumprod(self.alphas   , dim=0 )
       SCREAMING_SNAKE_CASE__       :			Optional[Any]													=torch.tensor(1.0 )

       # standard deviation of the initial noise distribution
       SCREAMING_SNAKE_CASE__       :			str													=1.0

       # setable values
       SCREAMING_SNAKE_CASE__       :			Optional[int]													=None
       SCREAMING_SNAKE_CASE__       :			int													=torch.from_numpy(np.arange(0   , __lowercase )[::-1].copy() )

       SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=variance_type




 def        __magic_name__		( self		:							Optional[int]   , __lowercase		:							torch.FloatTensor   , __lowercase		:							Optional[int] = None )		->  torch.FloatTensor:
       return sample




 def        __magic_name__		( self		:							Union[str, Any]   , __lowercase		:							int   , __lowercase		:							Union[str, torch.device] = None )		->  Union[str, Any]:
       SCREAMING_SNAKE_CASE__       :			List[str]													=num_inference_steps
       SCREAMING_SNAKE_CASE__       :			str													=(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
       SCREAMING_SNAKE_CASE__       :			Dict													=(np.arange(0   , __lowercase ) * step_ratio).round()[::-1].copy().astype(np.intaa )
       SCREAMING_SNAKE_CASE__       :			Optional[int]													=torch.from_numpy(__lowercase ).to(__lowercase )




 def        __magic_name__		( self		:							List[Any]   , __lowercase		:							str   , __lowercase		:							int=None   , __lowercase		:							Any=None   , __lowercase		:							Dict=None )		->  int:
       if prev_timestep is None:
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=t - 1

       SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=self.alphas_cumprod[t]
       SCREAMING_SNAKE_CASE__       :			int													=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       SCREAMING_SNAKE_CASE__       :			int													=1 - alpha_prod_t
       SCREAMING_SNAKE_CASE__       :			str													=1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
             SCREAMING_SNAKE_CASE__       :			str													=self.betas[t]
       else:
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=1 - alpha_prod_t / alpha_prod_t_prev

       # 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
       SCREAMING_SNAKE_CASE__       :			Optional[Any]													=beta_prod_t_prev / beta_prod_t * beta

       if variance_type is None:
             SCREAMING_SNAKE_CASE__       :			Dict													=self.config.variance_type

       # hacks - were probably added for training stability
       if variance_type == "fixed_small_log":
             SCREAMING_SNAKE_CASE__       :			Tuple													=torch.log(torch.clamp(__lowercase   , min=1e-20 ) )
             SCREAMING_SNAKE_CASE__       :			Tuple													=torch.exp(0.5 * variance )
       elif variance_type == "learned_range":
             # NOTE difference with DDPM scheduler
             SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=variance.log()
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=beta.log()

             SCREAMING_SNAKE_CASE__       :			List[str]													=(predicted_variance + 1) / 2
             SCREAMING_SNAKE_CASE__       :			List[Any]													=frac * max_log + (1 - frac) * min_log

       return variance




 def        __magic_name__		( self		:							Tuple   , __lowercase		:							torch.FloatTensor   , __lowercase		:							int   , __lowercase		:							torch.FloatTensor   , __lowercase		:							Optional[int] = None   , __lowercase		:							Dict=None   , __lowercase		:							bool = True   , )		->  Union[UnCLIPSchedulerOutput, Tuple]:
       SCREAMING_SNAKE_CASE__       :			Tuple													=timestep

       if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=torch.split(__lowercase   , sample.shape[1]   , dim=1 )
       else:
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=None

       # 1. compute alphas, betas
       if prev_timestep is None:
             SCREAMING_SNAKE_CASE__       :			Optional[int]													=t - 1

       SCREAMING_SNAKE_CASE__       :			List[Any]													=self.alphas_cumprod[t]
       SCREAMING_SNAKE_CASE__       :			str													=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       SCREAMING_SNAKE_CASE__       :			Any													=1 - alpha_prod_t
       SCREAMING_SNAKE_CASE__       :			Any													=1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
             SCREAMING_SNAKE_CASE__       :			Tuple													=self.betas[t]
             SCREAMING_SNAKE_CASE__       :			List[Any]													=self.alphas[t]
       else:
             SCREAMING_SNAKE_CASE__       :			List[str]													=1 - alpha_prod_t / alpha_prod_t_prev
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=1 - beta

       # 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":
             SCREAMING_SNAKE_CASE__       :			Tuple													=(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
       elif self.config.prediction_type == "sample":
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=model_output
       else:
             raise ValueError(
                 F"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
                 ''' for the UnCLIPScheduler.''' )

       # 3. Clip "predicted x_0"
       if self.config.clip_sample:
             SCREAMING_SNAKE_CASE__       :			Optional[Any]													=torch.clamp(
                 __lowercase   , -self.config.clip_sample_range   , self.config.clip_sample_range )

       # 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
       SCREAMING_SNAKE_CASE__       :			Tuple													=(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
       SCREAMING_SNAKE_CASE__       :			str													=alpha ** 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
       SCREAMING_SNAKE_CASE__       :			str													=pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

       # 6. Add noise
       SCREAMING_SNAKE_CASE__       :			Optional[int]													=0
       if t > 0:
             SCREAMING_SNAKE_CASE__       :			Dict													=randn_tensor(
                 model_output.shape   , dtype=model_output.dtype   , generator=__lowercase   , device=model_output.device )

             SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=self._get_variance(
                 __lowercase   , predicted_variance=__lowercase   , prev_timestep=__lowercase   , )

             if self.variance_type == "fixed_small_log":
                   SCREAMING_SNAKE_CASE__       :			str													=variance
             elif self.variance_type == "learned_range":
                   SCREAMING_SNAKE_CASE__       :			Optional[Any]													=(0.5 * variance).exp()
             else:
                   raise ValueError(
                       F"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
                       ''' for the UnCLIPScheduler.''' )

             SCREAMING_SNAKE_CASE__       :			Dict													=variance * variance_noise

       SCREAMING_SNAKE_CASE__       :			List[Any]													=pred_prev_sample + variance

       if not return_dict:
             return (pred_prev_sample,)

       return UnCLIPSchedulerOutput(prev_sample=__lowercase   , pred_original_sample=__lowercase )




 def        __magic_name__		( self		:							Any   , __lowercase		:							torch.FloatTensor   , __lowercase		:							torch.FloatTensor   , __lowercase		:							torch.IntTensor   , )		->  torch.FloatTensor:
       # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
       SCREAMING_SNAKE_CASE__       :			Dict													=self.alphas_cumprod.to(device=original_samples.device   , dtype=original_samples.dtype )
       SCREAMING_SNAKE_CASE__       :			str													=timesteps.to(original_samples.device )

       SCREAMING_SNAKE_CASE__       :			str													=alphas_cumprod[timesteps] ** 0.5
       SCREAMING_SNAKE_CASE__       :			str													=sqrt_alpha_prod.flatten()
       while len(sqrt_alpha_prod.shape ) < len(original_samples.shape ):
             SCREAMING_SNAKE_CASE__       :			List[str]													=sqrt_alpha_prod.unsqueeze(-1 )

       SCREAMING_SNAKE_CASE__       :			Dict													=(1 - alphas_cumprod[timesteps]) ** 0.5
       SCREAMING_SNAKE_CASE__       :			Tuple													=sqrt_one_minus_alpha_prod.flatten()
       while len(sqrt_one_minus_alpha_prod.shape ) < len(original_samples.shape ):
             SCREAMING_SNAKE_CASE__       :			Dict													=sqrt_one_minus_alpha_prod.unsqueeze(-1 )

       SCREAMING_SNAKE_CASE__       :			Optional[int]													=sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
       return noisy_samples







'''simple docstring'''
from __future__ import annotations

import os
from collections.abc import Mapping

a_					=	tuple[int, int]






class        __SCREAMING_SNAKE_CASE :




 def __init__( self		:							Any   , __lowercase		:							set[int]   , __lowercase		:							Mapping[EdgeT, int] )		->  None:
       SCREAMING_SNAKE_CASE__       :			set[int]													=vertices
       SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={
           (min(__lowercase ), max(__lowercase )): weight for edge, weight in edges.items()
       }




 def        __magic_name__		( self		:							Union[str, Any]   , __lowercase		:							EdgeT   , __lowercase		:							int )		->  None:
       self.vertices.add(edge[0] )
       self.vertices.add(edge[1] )
       SCREAMING_SNAKE_CASE__       :			List[str]													=weight




 def        __magic_name__		( self		:							Optional[Any] )		->  Graph:
       SCREAMING_SNAKE_CASE__       :			Graph													=Graph({min(self.vertices )}   , {} )
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int

       while len(subgraph.vertices ) < len(self.vertices ):
             SCREAMING_SNAKE_CASE__       :			Any													=max(self.edges.values() ) + 1
             for edge, weight in self.edges.items():
                   if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                         if weight < min_weight:
                               SCREAMING_SNAKE_CASE__       :			List[str]													=edge
                               SCREAMING_SNAKE_CASE__       :			Any													=weight

             subgraph.add_edge(__lowercase   , __lowercase )

       return subgraph





def 	_a(					UpperCamelCase__			:  str = "p107_network.txt"							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			str													=os.path.abspath(os.path.dirname(UpperCamelCase__							)							)
      SCREAMING_SNAKE_CASE__       :			str													=os.path.join(UpperCamelCase__,		UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={}
      SCREAMING_SNAKE_CASE__       :			list[str]
      SCREAMING_SNAKE_CASE__       :			int
      SCREAMING_SNAKE_CASE__       :			int

      with open(UpperCamelCase__							) as f:
            SCREAMING_SNAKE_CASE__       :			Any													=f.read().strip().split('''\n'''							)

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=[line.split(''','''							) for line in data]

      for edgea in range(1,		len(UpperCamelCase__							)							):
            for edgea in range(UpperCamelCase__							):
                  if adjaceny_matrix[edgea][edgea] != "-":
                        SCREAMING_SNAKE_CASE__       :			List[Any]													=int(adjaceny_matrix[edgea][edgea]							)

      SCREAMING_SNAKE_CASE__       :			Graph													=Graph(set(range(len(UpperCamelCase__							)							)							),		UpperCamelCase__							)

      SCREAMING_SNAKE_CASE__       :			Graph													=graph.prims_algorithm()

      SCREAMING_SNAKE_CASE__       :			int													=sum(graph.edges.values()							)
      SCREAMING_SNAKE_CASE__       :			int													=sum(subgraph.edges.values()							)

      return initial_total - optimal_total


if __name__ == "__main__":
  print(F'''{solution() = }''')