




'''simple docstring'''


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
def 	snake_case_					(UpperCamelCase :						List[Any]				,		UpperCamelCase :						str=0.999				,		UpperCamelCase :						Union[str, Any]="cosine"				,		):





							'''simple docstring'''


							if alpha_transform_type == "cosine":

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

							elif alpha_transform_type == "exp":

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

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

							_a			  =       []
							for i in range(UpperCamelCase   ):
														_a			  =       i / num_diffusion_timesteps
														_a			  =       (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     A					(	_a  ,_a					):
							lowercase_           =       [e.name for e in KarrasDiffusionSchedulers]
							lowercase_           =       2







							@register_to_config
							def __init__(						self :						List[str]							,    lowerCAmelCase_ :						int = 10_00							,    lowerCAmelCase_ :						float = 0.0_0_0_8_5							,    lowerCAmelCase_ :						float = 0.0_1_2							,    lowerCAmelCase_ :						str = "linear"							,    lowerCAmelCase_ :						Optional[Union[np.ndarray, List[float]]] = None							,    lowerCAmelCase_ :						str = "epsilon"							,    lowerCAmelCase_ :						Optional[bool] = False							,    lowerCAmelCase_ :						Optional[bool] = False							,    lowerCAmelCase_ :						float = 1.0							,    lowerCAmelCase_ :						str = "linspace"							,    lowerCAmelCase_ :						int = 0							,    )    ->							Dict:


														"""simple docstring"""


														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_							,    alpha_transform_type='''cosine'''      )
														elif beta_schedule == "exp":
																					_a			  =       betas_for_alpha_bar(lowerCAmelCase_							,    alpha_transform_type='''exp'''      )
														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      )

														#  set all values
														self.set_timesteps(lowerCAmelCase_							,    lowerCAmelCase_							,    lowerCAmelCase_      )
														_a			  =       use_karras_sigmas







							def      __lowerCAmelCase    (						self :						Tuple							,    lowerCAmelCase_ :						Any							,    lowerCAmelCase_ :						Any=None      )    ->							Optional[int]:


														"""simple docstring"""


														if schedule_timesteps is None:
																					_a			  =       self.timesteps

														_a			  =       (schedule_timesteps == timestep).nonzero()

														# The sigma index that is taken for the **very** first `step`
														# is always the second index (or the last index if there is only 1)
														# This way we can ensure we don't accidentally skip a sigma in
														# case we start in the middle of the denoising schedule (e.g. for image-to-image)
														if len(self._index_counter      ) == 0:
																					_a			  =       1 if len(lowerCAmelCase_      ) > 1 else 0
														else:
																					_a			  =       timestep.cpu().item() if torch.is_tensor(lowerCAmelCase_      ) else timestep
																					_a			  =       self._index_counter[timestep_int]

														return indices[pos].item()







							@property
							def      __lowerCAmelCase    (						self :						str      )    ->							int:


														"""simple docstring"""


														if self.config.timestep_spacing in ["linspace", "trailing"]:
																					return self.sigmas.max()

														return (self.sigmas.max() ** 2 + 1) ** 0.5







							def      __lowerCAmelCase    (						self :						Union[str, Any]							,    lowerCAmelCase_ :						torch.FloatTensor							,    lowerCAmelCase_ :						Union[float, torch.FloatTensor]							,    )    ->							torch.FloatTensor:


														"""simple docstring"""


														_a			  =       self.index_for_timestep(lowerCAmelCase_      )

														_a			  =       self.sigmas[step_index]
														_a			  =       sample / ((sigma**2 + 1) ** 0.5)
														return sample







							def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						int							,    lowerCAmelCase_ :						Union[str, torch.device] = None							,    lowerCAmelCase_ :						Optional[int] = None							,    )    ->							int:


														"""simple docstring"""


														_a			  =       num_inference_steps

														_a			  =       num_train_timesteps or self.config.num_train_timesteps

														# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
														if self.config.timestep_spacing == "linspace":
																					_a			  =       np.linspace(0							,    num_train_timesteps - 1							,    lowerCAmelCase_							,    dtype=lowerCAmelCase_      )[::-1].copy()
														elif self.config.timestep_spacing == "leading":
																					_a			  =       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()[::-1].copy().astype(lowerCAmelCase_      )
																					timesteps += self.config.steps_offset
														elif self.config.timestep_spacing == "trailing":
																					_a			  =       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(lowerCAmelCase_							,    0							,    -step_ratio      )).round().copy().astype(lowerCAmelCase_      )
																					timesteps -= 1
														else:
																					raise ValueError(
																					    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'      )

														_a			  =       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
														_a			  =       np.log(lowerCAmelCase_      )
														_a			  =       np.interp(lowerCAmelCase_							,    np.arange(0							,    len(lowerCAmelCase_      )      )							,    lowerCAmelCase_      )

														if self.config.use_karras_sigmas:
																					_a			  =       self._convert_to_karras(in_sigmas=lowerCAmelCase_							,    num_inference_steps=self.num_inference_steps      )
																					_a			  =       np.array([self._sigma_to_t(lowerCAmelCase_							,    lowerCAmelCase_      ) for sigma in sigmas]      )

														_a			  =       np.concatenate([sigmas, [0.0]]      ).astype(np.floataa      )
														_a			  =       torch.from_numpy(lowerCAmelCase_      ).to(device=lowerCAmelCase_      )
														_a			  =       torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2      ), sigmas[-1:]]      )

														_a			  =       torch.from_numpy(lowerCAmelCase_      )
														_a			  =       torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2      )]      )

														if str(lowerCAmelCase_      ).startswith('''mps'''      ):
																					# mps does not support float64
																					_a			  =       timesteps.to(lowerCAmelCase_							,    dtype=torch.floataa      )
														else:
																					_a			  =       timesteps.to(device=lowerCAmelCase_      )

														# empty dt and derivative
														_a			  =       None
														_a			  =       None

														# for exp beta schedules, such as the one for `pipeline_shap_e.py`
														# we need an index counter
														_a			  =       defaultdict(lowerCAmelCase_      )







							def      __lowerCAmelCase    (						self :						Tuple							,    lowerCAmelCase_ :						Any							,    lowerCAmelCase_ :						Dict      )    ->							Optional[Any]:


														"""simple docstring"""


														_a			  =       np.log(lowerCAmelCase_      )

														# get distribution
														_a			  =       log_sigma - log_sigmas[:, np.newaxis]

														# get sigmas range
														_a			  =       np.cumsum((dists >= 0)							,    axis=0      ).argmax(axis=0      ).clip(max=log_sigmas.shape[0] - 2      )
														_a			  =       low_idx + 1

														_a			  =       log_sigmas[low_idx]
														_a			  =       log_sigmas[high_idx]

														# interpolate sigmas
														_a			  =       (low - log_sigma) / (low - high)
														_a			  =       np.clip(lowerCAmelCase_							,    0							,    1      )

														# transform interpolation to time range
														_a			  =       (1 - w) * low_idx + w * high_idx
														_a			  =       t.reshape(sigma.shape      )
														return t







							def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						torch.FloatTensor							,    lowerCAmelCase_ :						Dict      )    ->							torch.FloatTensor:


														"""simple docstring"""


														_a			  =       in_sigmas[-1].item()
														_a			  =       in_sigmas[0].item()

														_a			  =       7.0  # 7.0 is the value used in the paper
														_a			  =       np.linspace(0							,    1							,    lowerCAmelCase_      )
														_a			  =       sigma_min ** (1 / rho)
														_a			  =       sigma_max ** (1 / rho)
														_a			  =       (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
														return sigmas







							@property
							def      __lowerCAmelCase    (						self :						int      )    ->							Optional[int]:


														"""simple docstring"""


														return self.dt is None







							def      __lowerCAmelCase    (						self :						str							,    lowerCAmelCase_ :						Union[torch.FloatTensor, np.ndarray]							,    lowerCAmelCase_ :						Union[float, torch.FloatTensor]							,    lowerCAmelCase_ :						Union[torch.FloatTensor, np.ndarray]							,    lowerCAmelCase_ :						bool = True							,    )    ->							Union[SchedulerOutput, Tuple]:


														"""simple docstring"""


														_a			  =       self.index_for_timestep(lowerCAmelCase_      )

														# advance index counter by 1
														_a			  =       timestep.cpu().item() if torch.is_tensor(lowerCAmelCase_      ) else timestep
														self._index_counter[timestep_int] += 1

														if self.state_in_first_order:
																					_a			  =       self.sigmas[step_index]
																					_a			  =       self.sigmas[step_index + 1]
														else:
																					# 2nd order / Heun's method
																					_a			  =       self.sigmas[step_index - 1]
																					_a			  =       self.sigmas[step_index]

														# currently only gamma=0 is supported. This usually works best anyways.
														# We can support gamma in the future but then need to scale the timestep before
														# passing it to the model which requires a change in API
														_a			  =       0
														_a			  =       sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

														# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
														if self.config.prediction_type == "epsilon":
																					_a			  =       sigma_hat if self.state_in_first_order else sigma_next
																					_a			  =       sample - sigma_input * model_output
														elif self.config.prediction_type == "v_prediction":
																					_a			  =       sigma_hat if self.state_in_first_order else sigma_next
																					_a			  =       model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
																					    sample / (sigma_input**2 + 1)
																					)
														elif self.config.prediction_type == "sample":
																					_a			  =       model_output
														else:
																					raise ValueError(
																					    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'      )

														if self.config.clip_sample:
																					_a			  =       pred_original_sample.clamp(
																					    -self.config.clip_sample_range							,    self.config.clip_sample_range      )

														if self.state_in_first_order:
																					# 2. Convert to an ODE derivative for 1st order
																					_a			  =       (sample - pred_original_sample) / sigma_hat
																					# 3. delta timestep
																					_a			  =       sigma_next - sigma_hat

																					# store for 2nd order step
																					_a			  =       derivative
																					_a			  =       dt
																					_a			  =       sample
														else:
																					# 2. 2nd order / Heun's method
																					_a			  =       (sample - pred_original_sample) / sigma_next
																					_a			  =       (self.prev_derivative + derivative) / 2

																					# 3. take prev timestep & sample
																					_a			  =       self.dt
																					_a			  =       self.sample

																					# free dt and derivative
																					# Note, this puts the scheduler in "first order mode"
																					_a			  =       None
																					_a			  =       None
																					_a			  =       None

														_a			  =       sample + derivative * dt

														if not return_dict:
																					return (prev_sample,)

														return SchedulerOutput(prev_sample=lowerCAmelCase_      )







							def      __lowerCAmelCase    (						self :						List[Any]							,    lowerCAmelCase_ :						torch.FloatTensor							,    lowerCAmelCase_ :						torch.FloatTensor							,    lowerCAmelCase_ :						torch.FloatTensor							,    )    ->							torch.FloatTensor:


														"""simple docstring"""


														_a			  =       self.sigmas.to(device=original_samples.device							,    dtype=original_samples.dtype      )
														if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase_      ):
																					# mps does not support float64
																					_a			  =       self.timesteps.to(original_samples.device							,    dtype=torch.floataa      )
																					_a			  =       timesteps.to(original_samples.device							,    dtype=torch.floataa      )
														else:
																					_a			  =       self.timesteps.to(original_samples.device      )
																					_a			  =       timesteps.to(original_samples.device      )

														_a			  =       [self.index_for_timestep(lowerCAmelCase_							,    lowerCAmelCase_      ) for t in timesteps]

														_a			  =       sigmas[step_indices].flatten()
														while len(sigma.shape      ) < len(original_samples.shape      ):
																					_a			  =       sigma.unsqueeze(-1      )

														_a			  =       original_samples + noise * sigma
														return noisy_samples







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


														"""simple docstring"""


														return self.config.num_train_timesteps







'''simple docstring'''


_snake_case   :   Any     							=	{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}
def 	snake_case_					(UpperCamelCase :						dict				,		UpperCamelCase :						Dict				,		UpperCamelCase :						Optional[int]   ):





							'''simple docstring'''


							_a			  =       set()
							# keep track of all the paths to be checked
							_a			  =       [[start]]

							# return path if start is goal
							if start == goal:
														return [start]

							# keeps looping until all possible paths have been checked
							while queue:
														# pop the first path from the queue
														_a			  =       queue.pop(0   )
														# get the last node from the path
														_a			  =       path[-1]
														if node not in explored:
																					_a			  =       graph[node]
																					# go through all neighbour nodes, construct a new path and
																					# push it into the queue
																					for neighbour in neighbours:
																												_a			  =       list(UpperCamelCase   )
																												new_path.append(UpperCamelCase   )
																												queue.append(UpperCamelCase   )
																												# return path if neighbour is goal
																												if neighbour == goal:
																																			return new_path

            # mark node as explored
																					explored.add(UpperCamelCase   )

    # in case there's no path between the 2 nodes
							return []
def 	snake_case_					(UpperCamelCase :						dict				,		UpperCamelCase :						Optional[int]				,		UpperCamelCase :						Dict   ):





							'''simple docstring'''


							if not graph or start not in graph or target not in graph:
														return -1
							if start == target:
														return 0
							_a			  =       [start]
							_a			  =       set(UpperCamelCase   )
							# Keep tab on distances from `start` node.
							_a			  =       {start: 0, target: -1}
							while queue:
														_a			  =       queue.pop(0   )
														if node == target:
																					_a			  =       (
																					    dist[node] if dist[target] == -1 else min(dist[target]				,		dist[node]   )
																					)
														for adjacent in graph[node]:
																					if adjacent not in visited:
																												visited.add(UpperCamelCase   )
																												queue.append(UpperCamelCase   )
																												_a			  =       dist[node] + 1
							return dist[target]


if __name__ == "__main__":
				print(bfs_shortest_path(demo_graph, 'G', 'D'))  # returns ['G', 'C', 'A', 'B', 'D']
				print(bfs_shortest_path_distance(demo_graph, 'G', 'D'))  # returns 4

