



'''simple docstring'''




# 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 						_UpperCamelCase  (							lowerCamelCase__    ):


			'''simple docstring'''

			_A      :		torch.FloatTensor
			_A      :		Optional[torch.FloatTensor]			    =		None


def 				lowerCAmelCase_   (	_lowerCamelCase:   Optional[int]       ,      _lowerCamelCase:   Optional[int]=0.9_99       ,      _lowerCamelCase:   int="cosine"       ,      ):
		if alpha_transform_type == "cosine":

				def alpha_bar_fn(_lowerCamelCase:   Tuple					):
						return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2					) ** 2

		elif alpha_transform_type == "exp":

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

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

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






class 						_UpperCamelCase  (							lowerCamelCase__    ,					lowerCamelCase__    ):


			'''simple docstring'''

			_A      :		Tuple			    =		1

			@register_to_config
			def __init__(							self     : Union[str, Any]							,     lowerCAmelCase__     : int = 1_0_0_0							,     lowerCAmelCase__     : float = 0.00_01							,     lowerCAmelCase__     : float = 0.02							,     lowerCAmelCase__     : str = "linear"							,     lowerCAmelCase__     : Optional[Union[np.ndarray, List[float]]] = None							,     lowerCAmelCase__     : bool = True							,     lowerCAmelCase__     : bool = True							,     lowerCAmelCase__     : int = 0							,     lowerCAmelCase__     : str = "epsilon"							,     lowerCAmelCase__     : float = 1.0							,     **lowerCAmelCase__     : Optional[int]							,     ):





					"""simple docstring"""






					if kwargs.get("""set_alpha_to_one"""							,     lowerCAmelCase__						) is not None:
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		(
							    """The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."""
							)
							deprecate("""set_alpha_to_one"""							,     """1.0.0"""							,     lowerCAmelCase__							,     standard_warn=lowerCAmelCase__						)
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		kwargs["""set_alpha_to_one"""]
					if trained_betas is not None:
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		torch.tensor(lowerCAmelCase__							,     dtype=torch.floataa						)
					elif beta_schedule == "linear":
							__SCREAMING_SNAKE_CASE       :		Dict           =		torch.linspace(lowerCAmelCase__							,     lowerCAmelCase__							,     lowerCAmelCase__							,     dtype=torch.floataa						)
					elif beta_schedule == "scaled_linear":
							# this schedule is very specific to the latent diffusion model.
							__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		(
							    torch.linspace(beta_start**0.5							,     beta_end**0.5							,     lowerCAmelCase__							,     dtype=torch.floataa						) ** 2
							)
					elif beta_schedule == "squaredcos_cap_v2":
							# Glide cosine schedule
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		betas_for_alpha_bar(lowerCAmelCase__						)
					else:
							raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"						)

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

					# standard deviation of the initial noise distribution
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		1.0

					# setable values
					__SCREAMING_SNAKE_CASE       :		int           =		None
					__SCREAMING_SNAKE_CASE       :		str           =		torch.from_numpy(np.arange(0							,     lowerCAmelCase__						).copy().astype(np.intaa						)						)

			def UpperCamelCase__					(							self     : int							,     lowerCAmelCase__     : torch.FloatTensor							,     lowerCAmelCase__     : Optional[int] = None						):





					"""simple docstring"""






					return sample

			def UpperCamelCase__					(							self     : Dict							,     lowerCAmelCase__     : int							,     lowerCAmelCase__     : Union[str, torch.device] = None						):





					"""simple docstring"""






					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."						)

					__SCREAMING_SNAKE_CASE       :		Dict           =		num_inference_steps
					__SCREAMING_SNAKE_CASE       :		Dict           =		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
					__SCREAMING_SNAKE_CASE       :		Tuple           =		(np.arange(0							,     lowerCAmelCase__						) * step_ratio).round().copy().astype(np.intaa						)
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		torch.from_numpy(lowerCAmelCase__						).to(lowerCAmelCase__						)
					self.timesteps += self.config.steps_offset

			def UpperCamelCase__					(							self     : Union[str, Any]							,     lowerCAmelCase__     : torch.FloatTensor							,     lowerCAmelCase__     : int							,     lowerCAmelCase__     : torch.FloatTensor							,     lowerCAmelCase__     : float = 0.0							,     lowerCAmelCase__     : bool = False							,     lowerCAmelCase__     : Optional[torch.FloatTensor] = None							,     lowerCAmelCase__     : bool = True							,     ):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		List[Any]           =		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
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		self.alphas_cumprod[timestep]
					__SCREAMING_SNAKE_CASE       :		int           =		(
					    self.alphas_cumprod[prev_timestep]
					    if prev_timestep < self.config.num_train_timesteps
					    else self.final_alpha_cumprod
					)

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



			def __len__(							self     : List[str]						):





					"""simple docstring"""






					return self.config.num_train_timesteps




'''simple docstring'''




from collections.abc import Iterable
from typing import Any






class 						_UpperCamelCase  :


			'''simple docstring'''

			def __init__(							self     : Optional[int]							,     lowerCAmelCase__     : int | None = None						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		value
					__SCREAMING_SNAKE_CASE       :		Node | None           =		None  # Added in order to delete a node easier
					__SCREAMING_SNAKE_CASE       :		Node | None           =		None
					__SCREAMING_SNAKE_CASE       :		Node | None           =		None



			def __repr__(							self     : Optional[Any]						):





					"""simple docstring"""






					from pprint import pformat

					if self.left is None and self.right is None:
							return str(self.value						)
					return pformat({F"{self.value}": (self.left, self.right)}							,     indent=1						)






class 						_UpperCamelCase  :


			'''simple docstring'''

			def __init__(							self     : Optional[int]							,     lowerCAmelCase__     : Node | None = None						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		str           =		root

			def __str__(							self     : Union[str, Any]						):





					"""simple docstring"""






					return str(self.root						)

			def UpperCamelCase__					(							self     : Dict							,     lowerCAmelCase__     : Node							,     lowerCAmelCase__     : Node | None						):





					"""simple docstring"""






					if new_children is not None:  # reset its kids
							__SCREAMING_SNAKE_CASE       :		List[str]           =		node.parent
					if node.parent is not None:  # reset its parent
							if self.is_right(lowerCAmelCase__						):  # If it is the right children
									__SCREAMING_SNAKE_CASE       :		Any           =		new_children
							else:
									__SCREAMING_SNAKE_CASE       :		int           =		new_children
					else:
							__SCREAMING_SNAKE_CASE       :		int           =		new_children

			def UpperCamelCase__					(							self     : str							,     lowerCAmelCase__     : Node						):





					"""simple docstring"""






					if node.parent and node.parent.right:
							return node == node.parent.right
					return False

			def UpperCamelCase__					(							self     : List[Any]						):





					"""simple docstring"""






					return self.root is None

			def UpperCamelCase__					(							self     : Optional[Any]							,     lowerCAmelCase__     : str						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		Node(lowerCAmelCase__						)  # create a new Node
					if self.empty():  # if Tree is empty
							__SCREAMING_SNAKE_CASE       :		Optional[int]           =		new_node  # set its root
					else:  # Tree is not empty
							__SCREAMING_SNAKE_CASE       :		Optional[int]           =		self.root  # from root
							if parent_node is None:
									return
							while True:  # While we don't get to a leaf
									if value < parent_node.value:  # We go left
											if parent_node.left is None:
													__SCREAMING_SNAKE_CASE       :		List[str]           =		new_node  # We insert the new node in a leaf
													break
											else:
													__SCREAMING_SNAKE_CASE       :		Any           =		parent_node.left
									else:
											if parent_node.right is None:
													__SCREAMING_SNAKE_CASE       :		Tuple           =		new_node
													break
											else:
													__SCREAMING_SNAKE_CASE       :		List[str]           =		parent_node.right
							__SCREAMING_SNAKE_CASE       :		Tuple           =		parent_node

			def UpperCamelCase__					(							self     : str							,     *lowerCAmelCase__     : List[Any]						):





					"""simple docstring"""






					for value in values:
							self.__insert(lowerCAmelCase__						)

			def UpperCamelCase__					(							self     : List[str]							,     lowerCAmelCase__     : Union[str, Any]						):





					"""simple docstring"""






					if self.empty():
							raise IndexError("""Warning: Tree is empty! please use another."""						)
					else:
							__SCREAMING_SNAKE_CASE       :		List[Any]           =		self.root
							# use lazy evaluation here to avoid NoneType Attribute error
							while node is not None and node.value is not value:
									__SCREAMING_SNAKE_CASE       :		Any           =		node.left if value < node.value else node.right
							return node

			def UpperCamelCase__					(							self     : List[Any]							,     lowerCAmelCase__     : Node | None = None						):





					"""simple docstring"""






					if node is None:
							if self.root is None:
									return None
							__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		self.root

					if not self.empty():
							while node.right is not None:
									__SCREAMING_SNAKE_CASE       :		Tuple           =		node.right
					return node

			def UpperCamelCase__					(							self     : Dict							,     lowerCAmelCase__     : Node | None = None						):





					"""simple docstring"""






					if node is None:
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		self.root
					if self.root is None:
							return None
					if not self.empty():
							__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		self.root
							while node.left is not None:
									__SCREAMING_SNAKE_CASE       :		Any           =		node.left
					return node

			def UpperCamelCase__					(							self     : str							,     lowerCAmelCase__     : int						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		List[str]           =		self.search(lowerCAmelCase__						)  # Look for the node with that label
					if node is not None:
							if node.left is None and node.right is None:  # If it has no children
									self.__reassign_nodes(lowerCAmelCase__							,     lowerCAmelCase__						)
							elif node.left is None:  # Has only right children
									self.__reassign_nodes(lowerCAmelCase__							,     node.right						)
							elif node.right is None:  # Has only left children
									self.__reassign_nodes(lowerCAmelCase__							,     node.left						)
							else:
									__SCREAMING_SNAKE_CASE       :		Tuple           =		self.get_max(
									    node.left						)  # Gets the max value of the left branch
									self.remove(tmp_node.value						)  # type: ignore
									__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		(
									    tmp_node.value  # type: ignore
									)  # Assigns the value to the node to delete and keep tree structure

			def UpperCamelCase__					(							self     : Tuple							,     lowerCAmelCase__     : Node | None						):





					"""simple docstring"""






					if node is not None:
							yield node  # Preorder Traversal
							yield from self.preorder_traverse(node.left						)
							yield from self.preorder_traverse(node.right						)

			def UpperCamelCase__					(							self     : Optional[int]							,     lowerCAmelCase__     : Optional[Any]=None						):





					"""simple docstring"""






					if traversal_function is None:
							return self.preorder_traverse(self.root						)
					else:
							return traversal_function(self.root						)

			def UpperCamelCase__					(							self     : str							,     lowerCAmelCase__     : list							,     lowerCAmelCase__     : Node | None						):





					"""simple docstring"""






					if node:
							self.inorder(lowerCAmelCase__							,     node.left						)
							arr.append(node.value						)
							self.inorder(lowerCAmelCase__							,     node.right						)



			def UpperCamelCase__					(							self     : int							,     lowerCAmelCase__     : int							,     lowerCAmelCase__     : Node						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		list[int]           =		[]
					self.inorder(lowerCAmelCase__							,     lowerCAmelCase__						)  # append all values to list using inorder traversal
					return arr[k - 1]


def 				lowerCAmelCase_   (	_lowerCamelCase:   Node | None					):
		__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		[]
		if curr_node is not None:
				__SCREAMING_SNAKE_CASE       :		Optional[int]           =		postorder(curr_node.left					) + postorder(curr_node.right					) + [curr_node]
		return node_list


def 				lowerCAmelCase_   (	):
		__SCREAMING_SNAKE_CASE       :		str           =		(8, 3, 6, 1, 10, 14, 13, 4, 7)
		__SCREAMING_SNAKE_CASE       :		Dict           =		BinarySearchTree()
		for i in testlist:
				t.insert(_lowerCamelCase					)

		# Prints all the elements of the list in order traversal
		print(_lowerCamelCase					)

		if t.search(6					) is not None:
				print("""The value 6 exists"""					)
		else:
				print("""The value 6 doesn't exist"""					)

		if t.search(-1					) is not None:
				print("""The value -1 exists"""					)
		else:
				print("""The value -1 doesn't exist"""					)

		if not t.empty():
				print("""Max Value: """       ,      t.get_max().value					)  # type: ignore
				print("""Min Value: """       ,      t.get_min().value					)  # type: ignore

		for i in testlist:
				t.remove(_lowerCamelCase					)
				print(_lowerCamelCase					)


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)