




# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
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  _lowerCAmelCase     (  _lowercase	):
      A__		     =		42
      A__		     =		None



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase=0.999	,      UpperCamelCase="cosine"	,      )     ->	Dict:
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(UpperCamelCase      ):
      return math.cos((t + 0.008) / 1.008 * math.pi / 2      ) ** 2

  elif alpha_transform_type == "exp":

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

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

  lowerCAmelCase__				:  str		       =     []
  for i in range(UpperCamelCase      ):
    lowerCAmelCase__				:  int		       =     i / num_diffusion_timesteps
    lowerCAmelCase__				:  Optional[int]		       =     (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  _lowerCAmelCase     (  _lowercase    ,			_lowercase	):
      A__		     =		1

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

        lowerCAmelCase__				:  List[str]		       =     1.0 - self.betas
        lowerCAmelCase__				:  List[str]		       =     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.
        lowerCAmelCase__				:  Dict		       =     torch.tensor(0.0		) if set_alpha_to_zero else self.alphas_cumprod[-1]

        # standard deviation of the initial noise distribution
        lowerCAmelCase__				:  int		       =     1.0

        # setable values
        lowerCAmelCase__				:  Tuple		       =     None
        lowerCAmelCase__				:  List[Any]		       =     torch.from_numpy(np.arange(0      ,				__UpperCAmelCase		).copy().astype(np.intaa		)		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase = None		):
        return sample

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase = 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."""		)

        lowerCAmelCase__				:  List[Any]		       =     num_inference_steps
        lowerCAmelCase__				:  Union[str, Any]		       =     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
        lowerCAmelCase__				:  Union[str, Any]		       =     (np.arange(0      ,				__UpperCAmelCase		) * step_ratio).round().copy().astype(np.intaa		)
        lowerCAmelCase__				:  int		       =     torch.from_numpy(__UpperCAmelCase		).to(__UpperCAmelCase		)
        self.timesteps += self.config.steps_offset

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase      ,				__UpperCAmelCase      ,				__UpperCAmelCase = 0.0      ,				__UpperCAmelCase = False      ,				__UpperCAmelCase = None      ,				__UpperCAmelCase = True      ,				):
        # 1. get previous step value (=t+1)
        lowerCAmelCase__				:  str		       =     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
        lowerCAmelCase__				:  List[Any]		       =     self.alphas_cumprod[timestep]
        lowerCAmelCase__				:  int		       =     (
            self.alphas_cumprod[prev_timestep]
            if prev_timestep < self.config.num_train_timesteps
            else self.final_alpha_cumprod
        )

        lowerCAmelCase__				:  Any		       =     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":
          lowerCAmelCase__				:  Union[str, Any]		       =     (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
          lowerCAmelCase__				:  Optional[Any]		       =     model_output
        elif self.config.prediction_type == "sample":
          lowerCAmelCase__				:  Optional[Any]		       =     model_output
          lowerCAmelCase__				:  str		       =     (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
        elif self.config.prediction_type == "v_prediction":
          lowerCAmelCase__				:  List[Any]		       =     (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
          lowerCAmelCase__				:  Any		       =     (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:
          lowerCAmelCase__				:  Optional[int]		       =     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
        lowerCAmelCase__				:  Dict		       =     (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
        lowerCAmelCase__				:  Union[str, Any]		       =     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=__UpperCAmelCase      ,				pred_original_sample=__UpperCAmelCase		)







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







lowerCAmelCase_					    = [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase      )     ->	int:
  # Return True if there is node that has not iterated.
  lowerCAmelCase__				:  List[str]		       =     [False] * len(UpperCamelCase      )
  lowerCAmelCase__				:  int		       =     [s]
  lowerCAmelCase__				:  Dict		       =     True

  while queue:
    lowerCAmelCase__				:  Union[str, Any]		       =     queue.pop(0      )
    for ind in range(len(graph[u]      )      ):
      if visited[ind] is False and graph[u][ind] > 0:
        queue.append(UpperCamelCase      )
        lowerCAmelCase__				:  List[str]		       =     True
        lowerCAmelCase__				:  int		       =     u

  return visited[t]



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase      )     ->	Optional[Any]:
  lowerCAmelCase__				:  Dict		       =     [-1] * (len(UpperCamelCase      ))
  lowerCAmelCase__				:  Dict		       =     0
  lowerCAmelCase__				:  List[str]		       =     []
  lowerCAmelCase__				:  Tuple		       =     [i[:] for i in graph]  # Record original cut, copy.
  while bfs(UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase      ):
    lowerCAmelCase__				:  Optional[Any]		       =     float('''Inf'''      )
    lowerCAmelCase__				:  Optional[Any]		       =     sink

    while s != source:
      # Find the minimum value in select path
      lowerCAmelCase__				:  Optional[Any]		       =     min(UpperCamelCase	,      graph[parent[s]][s]      )
      lowerCAmelCase__				:  Union[str, Any]		       =     parent[s]

    max_flow += path_flow
    lowerCAmelCase__				:  List[str]		       =     sink

    while v != source:
      lowerCAmelCase__				:  Union[str, Any]		       =     parent[v]
      graph[u][v] -= path_flow
      graph[v][u] += path_flow
      lowerCAmelCase__				:  Dict		       =     parent[v]

  for i in range(len(UpperCamelCase      )      ):
    for j in range(len(graph[0]      )      ):
      if graph[i][j] == 0 and temp[i][j] > 0:
        res.append((i, j)      )

  return res


if __name__ == "__main__":
     print(mincut(test_graph, source=0, sink=5))

