




"""simple docstring"""

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

import numpy as np
import torch

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


__lowerCamelCase								=						logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
class  _snake_case				(							lowerCamelCase__       ):

				'''simple docstring'''




				UpperCamelCase__		     =42



class  _snake_case				(							lowerCamelCase__							,						lowerCamelCase__       ):

				'''simple docstring'''




				UpperCamelCase__		     =1





				@register_to_config
				def __init__(							self      :  Dict					,							snake_case      :  str = 40					,							snake_case      :  Union[str, Any] = 0.002					,							snake_case      :  List[Any] = 80.0					,							snake_case      :  Optional[Any] = 0.5					,							snake_case      :  Any = 1.0					,							snake_case      :  Union[str, Any] = 7.0					,							snake_case      :  Tuple = True					,							):
								UpperCAmelCase_					:Optional[int]      			=      sigma_max

								UpperCAmelCase_					:Any      			=      np.linspace(0					,							1					,							lowercase_     )
								UpperCAmelCase_					:Optional[int]      			=      self._convert_to_karras(lowercase_     )
								UpperCAmelCase_					:str      			=      self.sigma_to_t(lowercase_     )

								# setable values
								UpperCAmelCase_					:str      			=      None
								UpperCAmelCase_					:List[str]      			=      torch.from_numpy(lowercase_     )
								UpperCAmelCase_					:List[Any]      			=      torch.from_numpy(lowercase_     )
								UpperCAmelCase_					:List[Any]      			=      False
								UpperCAmelCase_					:List[Any]      			=      False





				def 				snake_case_ (							self      :  Optional[int]					,							snake_case      :  str					,							snake_case      :  Optional[int]=None     ):






								if schedule_timesteps is None:
												UpperCAmelCase_					:str      			=      self.timesteps

								UpperCAmelCase_					:Tuple      			=      (schedule_timesteps == timestep).nonzero()
								return indices.item()





				def 				snake_case_ (							self      :  Union[str, Any]					,							snake_case      :  str					,							snake_case      :  int     ):






								if isinstance(lowercase_					,							torch.Tensor     ):
												UpperCAmelCase_					:Tuple      			=      timestep.to(self.timesteps.device     )
								UpperCAmelCase_					:Optional[Any]      			=      self.index_for_timestep(lowercase_     )
								UpperCAmelCase_					:int      			=      self.sigmas[step_idx]

								UpperCAmelCase_					:List[str]      			=      sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

								UpperCAmelCase_					:Dict      			=      True
								return sample





				def 				snake_case_ (							self      :  Any					,							snake_case      :  Optional[Any]     ):






								if not isinstance(lowercase_					,							np.ndarray     ):
												UpperCAmelCase_					:Union[str, Any]      			=      np.array(lowercase_					,							dtype=np.floataa     )

								UpperCAmelCase_					:List[str]      			=      1_000 * 0.25 * np.log(sigmas + 1e-44     )

								return timesteps





				def 				snake_case_ (							self      :  Dict					,							snake_case      :  Optional[int] = None					,							snake_case      :  str = None					,							snake_case      :  List[str] = None					,							):






								if num_inference_steps is None and timesteps is None:
												raise ValueError('''Exactly one of `num_inference_steps` or `timesteps` must be supplied.'''     )

								if num_inference_steps is not None and timesteps is not None:
												raise ValueError('''Can only pass one of `num_inference_steps` or `timesteps`.'''     )

								# Follow DDPMScheduler custom timesteps logic
								if timesteps is not None:
												for i in range(1					,							len(lowercase_     )     ):
																if timesteps[i] >= timesteps[i - 1]:
																				raise ValueError('''`timesteps` must be in descending order.'''     )

												if timesteps[0] >= self.config.num_train_timesteps:
																raise ValueError(
																    f'`timesteps` must start before `self.config.train_timesteps`:'
																    f' {self.config.num_train_timesteps}.'     )

												UpperCAmelCase_					:Union[str, Any]      			=      np.array(lowercase_					,							dtype=np.intaa     )
												UpperCAmelCase_					:List[str]      			=      True
								else:
												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.'     )

												UpperCAmelCase_					:Optional[int]      			=      num_inference_steps

												UpperCAmelCase_					:Tuple      			=      self.config.num_train_timesteps // self.num_inference_steps
												UpperCAmelCase_					:List[str]      			=      (np.arange(0					,							lowercase_     ) * step_ratio).round()[::-1].copy().astype(np.intaa     )
												UpperCAmelCase_					:Any      			=      False

								# Map timesteps to Karras sigmas directly for multistep sampling
								# See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
								UpperCAmelCase_					:int      			=      self.config.num_train_timesteps
								UpperCAmelCase_					:Tuple      			=      timesteps[::-1].copy()
								UpperCAmelCase_					:str      			=      ramp / (num_train_timesteps - 1)
								UpperCAmelCase_					:List[Any]      			=      self._convert_to_karras(lowercase_     )
								UpperCAmelCase_					:Optional[int]      			=      self.sigma_to_t(lowercase_     )

								UpperCAmelCase_					:Any      			=      np.concatenate([sigmas, [self.sigma_min]]     ).astype(np.floataa     )
								UpperCAmelCase_					:int      			=      torch.from_numpy(lowercase_     ).to(device=lowercase_     )

								if str(lowercase_     ).startswith('''mps'''     ):
												# mps does not support float64
												UpperCAmelCase_					:Optional[int]      			=      torch.from_numpy(lowercase_     ).to(lowercase_					,							dtype=torch.floataa     )
								else:
												UpperCAmelCase_					:Tuple      			=      torch.from_numpy(lowercase_     ).to(device=lowercase_     )





				def 				snake_case_ (							self      :  List[str]					,							snake_case      :  Any     ):
								UpperCAmelCase_					:Optional[int]      			=      self.config.sigma_min
								UpperCAmelCase_					:List[str]      			=      self.config.sigma_max

								UpperCAmelCase_					:Any      			=      self.config.rho
								UpperCAmelCase_					:Optional[int]      			=      sigma_min ** (1 / rho)
								UpperCAmelCase_					:List[Any]      			=      sigma_max ** (1 / rho)
								UpperCAmelCase_					:Tuple      			=      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
								return sigmas





				def 				snake_case_ (							self      :  Optional[Any]					,							snake_case      :  str     ):
								UpperCAmelCase_					:List[str]      			=      self.config.sigma_data

								UpperCAmelCase_					:Tuple      			=      sigma_data**2 / (sigma**2 + sigma_data**2)
								UpperCAmelCase_					:List[Any]      			=      sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
								return c_skip, c_out





				def 				snake_case_ (							self      :  Optional[Any]					,							snake_case      :  Tuple     ):
								UpperCAmelCase_					:Union[str, Any]      			=      self.config.sigma_min
								UpperCAmelCase_					:Tuple      			=      self.config.sigma_data

								UpperCAmelCase_					:Tuple      			=      sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
								UpperCAmelCase_					:List[Any]      			=      (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
								return c_skip, c_out





				def 				snake_case_ (							self      :  Dict					,							snake_case      :  Optional[Any]					,							snake_case      :  List[Any]					,							snake_case      :  Optional[int]					,							snake_case      :  int = None					,							snake_case      :  Any = True					,							):






								if (
								    isinstance(lowercase_					,							lowercase_     )
								    or isinstance(lowercase_					,							torch.IntTensor     )
								    or isinstance(lowercase_					,							torch.LongTensor     )
								):
												raise ValueError(
												    (
												        '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
												        f' `{self.__class__}.step()` is not supported. Make sure to pass'
												        ''' one of the `scheduler.timesteps` as a timestep.'''
												    )					,							)

								if not self.is_scale_input_called:
												logger.warning(
												    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
												    '''See `StableDiffusionPipeline` for a usage example.'''     )

								if isinstance(lowercase_					,							torch.Tensor     ):
												UpperCAmelCase_					:Union[str, Any]      			=      timestep.to(self.timesteps.device     )

								UpperCAmelCase_					:int      			=      self.config.sigma_min
								UpperCAmelCase_					:str      			=      self.config.sigma_max

								UpperCAmelCase_					:Optional[Any]      			=      self.index_for_timestep(lowercase_     )

								# sigma_next corresponds to next_t in original implementation
								UpperCAmelCase_					:int      			=      self.sigmas[step_index]
								if step_index + 1 < self.config.num_train_timesteps:
												UpperCAmelCase_					:int      			=      self.sigmas[step_index + 1]
								else:
												# Set sigma_next to sigma_min
												UpperCAmelCase_					:Optional[int]      			=      self.sigmas[-1]

								# Get scalings for boundary conditions
								UpperCAmelCase_			,UpperCAmelCase_					:Union[str, Any]      			=      self.get_scalings_for_boundary_condition(lowercase_     )

								# 1. Denoise model output using boundary conditions
								UpperCAmelCase_					:Optional[int]      			=      c_out * model_output + c_skip * sample
								if self.config.clip_denoised:
												UpperCAmelCase_					:Dict      			=      denoised.clamp(-1					,							1     )

								# 2. Sample z ~ N(0, s_noise^2 * I)
								# Noise is not used for onestep sampling.
								if len(self.timesteps     ) > 1:
												UpperCAmelCase_					:List[Any]      			=      randn_tensor(
												    model_output.shape					,							dtype=model_output.dtype					,							device=model_output.device					,							generator=lowercase_     )
								else:
												UpperCAmelCase_					:Tuple      			=      torch.zeros_like(lowercase_     )
								UpperCAmelCase_					:List[Any]      			=      noise * self.config.s_noise

								UpperCAmelCase_					:Optional[Any]      			=      sigma_next.clamp(min=lowercase_					,							max=lowercase_     )

								# 3. Return noisy sample
								# tau = sigma_hat, eps = sigma_min
								UpperCAmelCase_					:Optional[int]      			=      denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

								if not return_dict:
												return (prev_sample,)

								return CMStochasticIterativeSchedulerOutput(prev_sample=lowercase_     )





				def 				snake_case_ (							self      :  str					,							snake_case      :  List[str]					,							snake_case      :  Union[str, Any]					,							snake_case      :  Union[str, Any]					,							):
								UpperCAmelCase_					:Dict      			=      self.sigmas.to(device=original_samples.device					,							dtype=original_samples.dtype     )
								if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_     ):
												# mps does not support float64
												UpperCAmelCase_					:Union[str, Any]      			=      self.timesteps.to(original_samples.device					,							dtype=torch.floataa     )
												UpperCAmelCase_					:str      			=      timesteps.to(original_samples.device					,							dtype=torch.floataa     )
								else:
												UpperCAmelCase_					:str      			=      self.timesteps.to(original_samples.device     )
												UpperCAmelCase_					:Tuple      			=      timesteps.to(original_samples.device     )

								UpperCAmelCase_					:Optional[int]      			=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

								UpperCAmelCase_					:Any      			=      sigmas[step_indices].flatten()
								while len(sigma.shape     ) < len(original_samples.shape     ):
												UpperCAmelCase_					:Union[str, Any]      			=      sigma.unsqueeze(-1     )

								UpperCAmelCase_					:Tuple      			=      original_samples + noise * sigma
								return noisy_samples





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








"""simple docstring"""

# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint



class  _snake_case				:

				'''simple docstring'''




				def __init__(							self      :  str					,							snake_case      :  Optional[Any]					,							snake_case      :  str     ):
								UpperCAmelCase_					:Union[str, Any]      			=      key
								UpperCAmelCase_					:str      			=      freq





				def __str__(							self      :  Optional[Any]     ):
								return f'Node(key={self.key}, freq={self.freq})'



def 				a (						__snake_case     :				int,    __snake_case     :				Optional[int],    __snake_case     :				Tuple,    __snake_case     :				Any,    __snake_case     :				Dict,    __snake_case     :				List[str]  ):



				'''simple docstring'''





				if i > j or i < 0 or j > len(__snake_case  ) - 1:
								return

				UpperCAmelCase_					:List[str]      			=      root[i][j]
				if parent == -1:  # root does not have a parent
								print(f'{key[node]} is the root of the binary search tree.'  )
				elif is_left:
								print(f'{key[node]} is the left child of key {parent}.'  )
				else:
								print(f'{key[node]} is the right child of key {parent}.'  )

				print_binary_search_tree(__snake_case,    __snake_case,    __snake_case,    node - 1,    key[node],    __snake_case  )
				print_binary_search_tree(__snake_case,    __snake_case,    node + 1,    __snake_case,    key[node],    __snake_case  )



def 				a (						__snake_case     :				Optional[Any]  ):



				'''simple docstring'''





				nodes.sort(key=lambda __snake_case  : node.key  )

				UpperCAmelCase_					:List[str]      			=      len(__snake_case  )

				UpperCAmelCase_					:Any      			=      [nodes[i].key for i in range(__snake_case  )]
				UpperCAmelCase_					:int      			=      [nodes[i].freq for i in range(__snake_case  )]

				# This 2D array stores the overall tree cost (which's as minimized as possible);
				# for a single key, cost is equal to frequency of the key.
				UpperCAmelCase_					:Dict      			=      [[freqs[i] if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]
				# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
				# array
				UpperCAmelCase_					:Optional[Any]      			=      [[freqs[i] if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]
				# stores tree roots that will be used later for constructing binary search tree
				UpperCAmelCase_					:int      			=      [[i if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]

				for interval_length in range(2,    n + 1  ):
								for i in range(n - interval_length + 1  ):
												UpperCAmelCase_					:Union[str, Any]      			=      i + interval_length - 1

												UpperCAmelCase_					:Optional[int]      			=      sys.maxsize  # set the value to "infinity"
												UpperCAmelCase_					:List[Any]      			=      total[i][j - 1] + freqs[j]

												# Apply Knuth's optimization
												# Loop without optimization: for r in range(i, j + 1):
												for r in range(root[i][j - 1],    root[i + 1][j] + 1  ):  # r is a temporal root
																UpperCAmelCase_					:Any      			=      dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
																UpperCAmelCase_					:Optional[int]      			=      dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
																UpperCAmelCase_					:Union[str, Any]      			=      left + total[i][j] + right

																if dp[i][j] > cost:
																				UpperCAmelCase_					:Optional[Any]      			=      cost
																				UpperCAmelCase_					:Optional[int]      			=      r

				print('''Binary search tree nodes:'''  )
				for node in nodes:
								print(__snake_case  )

				print(f'\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'  )
				print_binary_search_tree(__snake_case,    __snake_case,    0,    n - 1,    -1,    __snake_case  )



def 				a (						):



				'''simple docstring'''





				UpperCAmelCase_					:Union[str, Any]      			=      [Node(__snake_case,    randint(1,    50  )  ) for i in range(10,    0,    -1  )]
				find_optimal_binary_search_tree(__snake_case  )


if __name__ == "__main__":
						main()


