'''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     __magic_name__						(    _UpperCAmelCase):
			UpperCamelCase__				=       42
			UpperCamelCase__				=       None




def 							lowerCamelCase	(      UpperCAmelCase__       :					Dict      ,      UpperCAmelCase__       :					str=0.999      ,      UpperCAmelCase__       :					List[str]="cosine"      ,      )			->      int:
							if alpha_transform_type == "cosine":

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

							elif alpha_transform_type == "exp":

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

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

							lowercase_					:			Optional[Any]										=       []
							for i in range(UpperCAmelCase__ ):
														lowercase_					:			Union[str, Any]										=       i / num_diffusion_timesteps
														lowercase_					:			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     __magic_name__						(    _UpperCAmelCase,     _UpperCAmelCase):







			@register_to_config
			def __init__(	self				:  List[Any]				,			lowercase_				:  int = 1000				,			lowercase_				:  str = "fixed_small_log"				,			lowercase_				:  bool = True				,			lowercase_				:  Optional[float] = 1.0				,			lowercase_				:  str = "epsilon"				,			lowercase_				:  str = "squaredcos_cap_v2"				,			):
										if beta_schedule != "squaredcos_cap_v2":
																	raise ValueError("""UnCLIPScheduler only supports `beta_schedule`: 'squaredcos_cap_v2'"""    )

										lowercase_					:			Any										=       betas_for_alpha_bar(lowercase_    )

										lowercase_					:			Dict										=       1.0 - self.betas
										lowercase_					:			List[str]										=       torch.cumprod(self.alphas				,			dim=0    )
										lowercase_					:			Optional[int]										=       torch.tensor(1.0    )

										# standard deviation of the initial noise distribution
										lowercase_					:			List[Any]										=       1.0

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

										lowercase_					:			int										=       variance_type







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any				,			lowercase_				:  torch.FloatTensor				,			lowercase_				:  Optional[int] = None    ):
										return sample







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







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Optional[int]				,			lowercase_				:  List[Any]				,			lowercase_				:  Tuple=None				,			lowercase_				:  List[str]=None				,			lowercase_				:  Optional[Any]=None    ):
										if prev_timestep is None:
																	lowercase_					:			Any										=       t - 1

										lowercase_					:			int										=       self.alphas_cumprod[t]
										lowercase_					:			Optional[Any]										=       self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
										lowercase_					:			Dict										=       1 - alpha_prod_t
										lowercase_					:			str										=       1 - alpha_prod_t_prev

										if prev_timestep == t - 1:
																	lowercase_					:			Any										=       self.betas[t]
										else:
																	lowercase_					:			str										=       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
										lowercase_					:			Union[str, Any]										=       beta_prod_t_prev / beta_prod_t * beta

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

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

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

										return variance







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple				,			lowercase_				:  torch.FloatTensor				,			lowercase_				:  int				,			lowercase_				:  torch.FloatTensor				,			lowercase_				:  Optional[int] = None				,			lowercase_				:  List[str]=None				,			lowercase_				:  bool = True				,			):
										lowercase_					:			Union[str, Any]										=       timestep

										if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
																	lowercase_						,						lowercase_					:			List[str]										=       torch.split(lowercase_				,			sample.shape[1]				,			dim=1    )
										else:
																	lowercase_					:			List[str]										=       None

										# 1. compute alphas, betas
										if prev_timestep is None:
																	lowercase_					:			str										=       t - 1

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

										if prev_timestep == t - 1:
																	lowercase_					:			List[Any]										=       self.betas[t]
																	lowercase_					:			str										=       self.alphas[t]
										else:
																	lowercase_					:			Optional[Any]										=       1 - alpha_prod_t / alpha_prod_t_prev
																	lowercase_					:			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":
																	lowercase_					:			List[str]										=       (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
										elif self.config.prediction_type == "sample":
																	lowercase_					:			Dict										=       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:
																	lowercase_					:			str										=       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
										lowercase_					:			List[Any]										=       (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
										lowercase_					:			Dict										=       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
										lowercase_					:			Optional[Any]										=       pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

										# 6. Add noise
										lowercase_					:			Dict										=       0
										if t > 0:
																	lowercase_					:			Tuple										=       randn_tensor(
																	    model_output.shape				,			dtype=model_output.dtype				,			generator=lowercase_				,			device=model_output.device    )

																	lowercase_					:			Any										=       self._get_variance(
																	    lowercase_				,			predicted_variance=lowercase_				,			prev_timestep=lowercase_				,			)

																	if self.variance_type == "fixed_small_log":
																								lowercase_					:			Optional[int]										=       variance
																	elif self.variance_type == "learned_range":
																								lowercase_					:			int										=       (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."""    )

																	lowercase_					:			Dict										=       variance * variance_noise

										lowercase_					:			List[str]										=       pred_prev_sample + variance

										if not return_dict:
																	return (pred_prev_sample,)

										return UnCLIPSchedulerOutput(prev_sample=lowercase_				,			pred_original_sample=lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[str]				,			lowercase_				:  torch.FloatTensor				,			lowercase_				:  torch.FloatTensor				,			lowercase_				:  torch.IntTensor				,			):
										# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
										lowercase_					:			Union[str, Any]										=       self.alphas_cumprod.to(device=original_samples.device				,			dtype=original_samples.dtype    )
										lowercase_					:			List[Any]										=       timesteps.to(original_samples.device    )

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

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

										lowercase_					:			int										=       sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
										return noisy_samples






'''simple docstring'''




from __future__ import annotations

import math
import random
from typing import Any





class     __magic_name__						:







			def __init__(	self				:  Any    ):
										lowercase_					:			list[Any]										=       []
										lowercase_					:			int										=       0
										lowercase_					:			int										=       0







			def 	SCREAMING_SNAKE_CASE_     (	self				:  int    ):
										return self.head == self.tail







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[str]				,			lowercase_				:  Any    ):
										self.data.append(lowercase_    )
										lowercase_					:			Optional[Any]										=       self.tail + 1







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Optional[Any]    ):
										lowercase_					:			List[Any]										=       self.data[self.head]
										lowercase_					:			Optional[int]										=       self.head + 1
										return ret







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[str]    ):
										return self.tail - self.head







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple    ):
										print(self.data    )
										print("""**************"""    )
										print(self.data[self.head : self.tail]    )





class     __magic_name__						:







			def __init__(	self				:  Any				,			lowercase_				:  Any    ):
										lowercase_					:			Optional[Any]										=       data
										lowercase_					:			MyNode | None										=       None
										lowercase_					:			MyNode | None										=       None
										lowercase_					:			int										=       1







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple    ):
										return self.data







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Union[str, Any]    ):
										return self.left







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Dict    ):
										return self.right







			def 	SCREAMING_SNAKE_CASE_     (	self				:  str    ):
										return self.height







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any				,			lowercase_				:  Any    ):
										lowercase_					:			Dict										=       data







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Union[str, Any]				,			lowercase_				:  MyNode | None    ):
										lowercase_					:			Optional[Any]										=       node







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple				,			lowercase_				:  MyNode | None    ):
										lowercase_					:			str										=       node







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any				,			lowercase_				:  int    ):
										lowercase_					:			Tuple										=       height




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode | None )			->      int:
							if node is None:
														return 0
							return node.get_height()




def 							lowerCamelCase	(      UpperCAmelCase__       :					int      ,      UpperCAmelCase__       :					int )			->      int:
							if a > b:
														return a
							return b




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      MyNode:
							print("""left rotation node:"""      ,      node.get_data() )
							lowercase_					:			Union[str, Any]										=       node.get_left()
							assert ret is not None
							node.set_left(ret.get_right() )
							ret.set_right(UpperCAmelCase__ )
							lowercase_					:			Any										=       my_max(get_height(node.get_right() )      ,      get_height(node.get_left() ) ) + 1
							node.set_height(UpperCAmelCase__ )
							lowercase_					:			Optional[int]										=       my_max(get_height(ret.get_right() )      ,      get_height(ret.get_left() ) ) + 1
							ret.set_height(UpperCAmelCase__ )
							return ret




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      MyNode:
							print("""right rotation node:"""      ,      node.get_data() )
							lowercase_					:			Dict										=       node.get_right()
							assert ret is not None
							node.set_right(ret.get_left() )
							ret.set_left(UpperCAmelCase__ )
							lowercase_					:			Tuple										=       my_max(get_height(node.get_right() )      ,      get_height(node.get_left() ) ) + 1
							node.set_height(UpperCAmelCase__ )
							lowercase_					:			str										=       my_max(get_height(ret.get_right() )      ,      get_height(ret.get_left() ) ) + 1
							ret.set_height(UpperCAmelCase__ )
							return ret




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      MyNode:
							lowercase_					:			Optional[Any]										=       node.get_left()
							assert left_child is not None
							node.set_left(left_rotation(UpperCAmelCase__ ) )
							return right_rotation(UpperCAmelCase__ )




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      MyNode:
							lowercase_					:			Optional[Any]										=       node.get_right()
							assert right_child is not None
							node.set_right(right_rotation(UpperCAmelCase__ ) )
							return left_rotation(UpperCAmelCase__ )




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode | None      ,      UpperCAmelCase__       :					Any )			->      MyNode | None:
							if node is None:
														return MyNode(UpperCAmelCase__ )
							if data < node.get_data():
														node.set_left(insert_node(node.get_left()      ,      UpperCAmelCase__ ) )
														if (
														    get_height(node.get_left() ) - get_height(node.get_right() ) == 2
														):  # an unbalance detected
																					lowercase_					:			List[Any]										=       node.get_left()
																					assert left_child is not None
																					if (
																					    data < left_child.get_data()
																					):  # new node is the left child of the left child
																												lowercase_					:			List[Any]										=       right_rotation(UpperCAmelCase__ )
																					else:
																												lowercase_					:			Any										=       lr_rotation(UpperCAmelCase__ )
							else:
														node.set_right(insert_node(node.get_right()      ,      UpperCAmelCase__ ) )
														if get_height(node.get_right() ) - get_height(node.get_left() ) == 2:
																					lowercase_					:			Any										=       node.get_right()
																					assert right_child is not None
																					if data < right_child.get_data():
																												lowercase_					:			Optional[int]										=       rl_rotation(UpperCAmelCase__ )
																					else:
																												lowercase_					:			Optional[int]										=       left_rotation(UpperCAmelCase__ )
							lowercase_					:			Optional[int]										=       my_max(get_height(node.get_right() )      ,      get_height(node.get_left() ) ) + 1
							node.set_height(UpperCAmelCase__ )
							return node




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      Any:
							while True:
														lowercase_					:			Any										=       root.get_right()
														if right_child is None:
																					break
														lowercase_					:			List[str]										=       right_child
							return root.get_data()




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode )			->      Any:
							while True:
														lowercase_					:			List[Any]										=       root.get_left()
														if left_child is None:
																					break
														lowercase_					:			str										=       left_child
							return root.get_data()




def 							lowerCamelCase	(      UpperCAmelCase__       :					MyNode      ,      UpperCAmelCase__       :					Any )			->      MyNode | None:
							lowercase_					:			Union[str, Any]										=       root.get_left()
							lowercase_					:			int										=       root.get_right()
							if root.get_data() == data:
														if left_child is not None and right_child is not None:
																					lowercase_					:			Any										=       get_left_most(UpperCAmelCase__ )
																					root.set_data(UpperCAmelCase__ )
																					root.set_right(del_node(UpperCAmelCase__      ,      UpperCAmelCase__ ) )
														elif left_child is not None:
																					lowercase_					:			Dict										=       left_child
														elif right_child is not None:
																					lowercase_					:			Dict										=       right_child
														else:
																					return None
							elif root.get_data() > data:
														if left_child is None:
																					print("""No such data""" )
																					return root
														else:
																					root.set_left(del_node(UpperCAmelCase__      ,      UpperCAmelCase__ ) )
							else:  # root.get_data() < data
														if right_child is None:
																					return root
														else:
																					root.set_right(del_node(UpperCAmelCase__      ,      UpperCAmelCase__ ) )

							if get_height(UpperCAmelCase__ ) - get_height(UpperCAmelCase__ ) == 2:
														assert right_child is not None
														if get_height(right_child.get_right() ) > get_height(right_child.get_left() ):
																					lowercase_					:			str										=       left_rotation(UpperCAmelCase__ )
														else:
																					lowercase_					:			List[str]										=       rl_rotation(UpperCAmelCase__ )
							elif get_height(UpperCAmelCase__ ) - get_height(UpperCAmelCase__ ) == -2:
														assert left_child is not None
														if get_height(left_child.get_left() ) > get_height(left_child.get_right() ):
																					lowercase_					:			Optional[Any]										=       right_rotation(UpperCAmelCase__ )
														else:
																					lowercase_					:			List[str]										=       lr_rotation(UpperCAmelCase__ )
							lowercase_					:			int										=       my_max(get_height(root.get_right() )      ,      get_height(root.get_left() ) ) + 1
							root.set_height(UpperCAmelCase__ )
							return root





class     __magic_name__						:







			def __init__(	self				:  List[str]    ):
										lowercase_					:			MyNode | None										=       None







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Optional[int]    ):
										return get_height(self.root    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any				,			lowercase_				:  Any    ):
										print("""insert:""" + str(lowercase_    )    )
										lowercase_					:			Dict										=       insert_node(self.root				,			lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any				,			lowercase_				:  Any    ):
										print("""delete:""" + str(lowercase_    )    )
										if self.root is None:
																	print("""Tree is empty!"""    )
																	return
										lowercase_					:			int										=       del_node(self.root				,			lowercase_    )







			def __str__(	self				:  Optional[int]				,			):  # a level traversale, gives a more intuitive look on the tree
										lowercase_					:			int										=       """"""
										lowercase_					:			Optional[int]										=       MyQueue()
										q.push(self.root    )
										lowercase_					:			Optional[Any]										=       self.get_height()
										if layer == 0:
																	return output
										lowercase_					:			Optional[int]										=       0
										while not q.is_empty():
																	lowercase_					:			Any										=       q.pop()
																	lowercase_					:			List[Any]										=       """ """ * int(math.pow(2				,			layer - 1    )    )
																	output += space
																	if node is None:
																								output += "*"
																								q.push(lowercase_    )
																								q.push(lowercase_    )
																	else:
																								output += str(node.get_data()    )
																								q.push(node.get_left()    )
																								q.push(node.get_right()    )
																	output += space
																	lowercase_					:			Union[str, Any]										=       cnt + 1
																	for i in range(100    ):
																								if cnt == math.pow(2				,			lowercase_    ) - 1:
																															lowercase_					:			Optional[Any]										=       layer - 1
																															if layer == 0:
																																						output += "\n*************************************"
																																						return output
																															output += "\n"
																															break
										output += "\n*************************************"
										return output




def 							lowerCamelCase	(      )			->      None:
							import doctest

							doctest.testmod()


if __name__ == "__main__":
						_test()
						_lowercase						: Optional[Any]						=						AVLtree()
						_lowercase						: Optional[Any]						=						list(range(10))
						random.shuffle(lst)
						for i in lst:
												t.insert(i)
												print(str(t))
						random.shuffle(lst)
						for i in lst:
												t.del_node(i)
												print(str(t))





