




"""simple docstring"""

import torch

from diffusers import EulerAncestralDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest

class 							lowercase   (     __UpperCAmelCase):
				__lowerCAmelCase     :     Tuple								= (EulerAncestralDiscreteScheduler,)
				__lowerCAmelCase     :     str								= 10







				def        a_	(				self :       Optional[int]   ,  **_lowerCamelCase :       List[str]							):



					"""simple docstring"""

					A_	:					Any						 =		{
					    '''num_train_timesteps''': 11_00,
					    '''beta_start''': 0.0001,
					    '''beta_end''': 0.02,
					    '''beta_schedule''': '''linear''',
					}

					config.update(**_lowerCamelCase							)
					return config







				def        a_	(				self :       Dict							):



					"""simple docstring"""

					for timesteps in [10, 50, 1_00, 10_00]:
						self.check_over_configs(num_train_timesteps=_lowerCamelCase							)







				def        a_	(				self :       Optional[Any]							):



					"""simple docstring"""

					for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]   ,  [0.0002, 0.002, 0.02]							):
						self.check_over_configs(beta_start=_lowerCamelCase   ,  beta_end=_lowerCamelCase							)







				def        a_	(				self :       List[str]							):



					"""simple docstring"""

					for schedule in ["linear", "scaled_linear"]:
						self.check_over_configs(beta_schedule=_lowerCamelCase							)







				def        a_	(				self :       Tuple							):



					"""simple docstring"""

					for prediction_type in ["epsilon", "v_prediction"]:
						self.check_over_configs(prediction_type=_lowerCamelCase							)







				def        a_	(				self :       Any							):



					"""simple docstring"""

					A_	:					Optional[int]						 =		self.scheduler_classes[0]
					A_	:					Union[str, Any]						 =		self.get_scheduler_config()
					A_	:					str						 =		scheduler_class(**_lowerCamelCase							)

					scheduler.set_timesteps(self.num_inference_steps							)

					A_	:					Optional[Any]						 =		torch.manual_seed(0							)

					A_	:					List[str]						 =		self.dummy_model()
					A_	:					Dict						 =		self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
					A_	:					Tuple						 =		sample.to(_lowerCamelCase							)

					for i, t in enumerate(scheduler.timesteps							):
						A_	:					Dict						 =		scheduler.scale_model_input(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					List[Any]						 =		model(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					List[Any]						 =		scheduler.step(_lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase   ,  generator=_lowerCamelCase							)
						A_	:					Optional[int]						 =		output.prev_sample

					A_	:					int						 =		torch.sum(torch.abs(_lowerCamelCase							)							)
					A_	:					Dict						 =		torch.mean(torch.abs(_lowerCamelCase							)							)

					assert abs(result_sum.item() - 152.3192							) < 1E-2
					assert abs(result_mean.item() - 0.1983							) < 1E-3







				def        a_	(				self :       List[str]							):



					"""simple docstring"""

					A_	:					int						 =		self.scheduler_classes[0]
					A_	:					Tuple						 =		self.get_scheduler_config(prediction_type='''v_prediction'''							)
					A_	:					Any						 =		scheduler_class(**_lowerCamelCase							)

					scheduler.set_timesteps(self.num_inference_steps							)

					A_	:					Union[str, Any]						 =		torch.manual_seed(0							)

					A_	:					List[Any]						 =		self.dummy_model()
					A_	:					Dict						 =		self.dummy_sample_deter * scheduler.init_noise_sigma
					A_	:					Any						 =		sample.to(_lowerCamelCase							)

					for i, t in enumerate(scheduler.timesteps							):
						A_	:					Optional[Any]						 =		scheduler.scale_model_input(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					List[str]						 =		model(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					Any						 =		scheduler.step(_lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase   ,  generator=_lowerCamelCase							)
						A_	:					Any						 =		output.prev_sample

					A_	:					List[str]						 =		torch.sum(torch.abs(_lowerCamelCase							)							)
					A_	:					List[Any]						 =		torch.mean(torch.abs(_lowerCamelCase							)							)

					assert abs(result_sum.item() - 108.4439							) < 1E-2
					assert abs(result_mean.item() - 0.1412							) < 1E-3







				def        a_	(				self :       Any							):



					"""simple docstring"""

					A_	:					Any						 =		self.scheduler_classes[0]
					A_	:					int						 =		self.get_scheduler_config()
					A_	:					List[str]						 =		scheduler_class(**_lowerCamelCase							)

					scheduler.set_timesteps(self.num_inference_steps   ,  device=_lowerCamelCase							)
					A_	:					Optional[Any]						 =		torch.manual_seed(0							)

					A_	:					List[str]						 =		self.dummy_model()
					A_	:					Any						 =		self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
					A_	:					Optional[int]						 =		sample.to(_lowerCamelCase							)

					for t in scheduler.timesteps:
						A_	:					str						 =		scheduler.scale_model_input(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					Union[str, Any]						 =		model(_lowerCamelCase   ,  _lowerCamelCase							)

						A_	:					str						 =		scheduler.step(_lowerCamelCase   ,  _lowerCamelCase   ,  _lowerCamelCase   ,  generator=_lowerCamelCase							)
						A_	:					List[str]						 =		output.prev_sample

					A_	:					Optional[int]						 =		torch.sum(torch.abs(_lowerCamelCase							)							)
					A_	:					int						 =		torch.mean(torch.abs(_lowerCamelCase							)							)

					assert abs(result_sum.item() - 152.3192							) < 1E-2
					assert abs(result_mean.item() - 0.1983							) < 1E-3











"""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 							lowercase   :







				def __init__(				self :       Optional[int]   ,  _lowerCamelCase :       str   ,  _lowerCamelCase :       Optional[Any]							):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		key
					A_	:					str						 =		freq







				def __str__(				self :       Optional[Any]							):



					"""simple docstring"""

					return F"""Node(key={self.key}, freq={self.freq})"""

def 		lowercase_   (		_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase						):




	"""simple docstring"""






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

	A_	:					Union[str, Any]						 =		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(_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   node - 1	,   key[node]	,   _UpperCAmelCase						)
	print_binary_search_tree(_UpperCAmelCase	,   _UpperCAmelCase	,   node + 1	,   _UpperCAmelCase	,   key[node]	,   _UpperCAmelCase						)

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






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

	A_	:					Any						 =		len(_UpperCAmelCase						)

	A_	:					int						 =		[nodes[i].key for i in range(_UpperCAmelCase						)]
	A_	:					List[str]						 =		[nodes[i].freq for i in range(_UpperCAmelCase						)]

	# 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.
	A_	:					List[str]						 =		[[freqs[i] if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]
	# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
	# array
	A_	:					Optional[int]						 =		[[freqs[i] if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]
	# stores tree roots that will be used later for constructing binary search tree
	A_	:					List[Any]						 =		[[i if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]

	for interval_length in range(2	,   n + 1						):
		for i in range(n - interval_length + 1						):
			A_	:					List[Any]						 =		i + interval_length - 1

			A_	:					List[Any]						 =		sys.maxsize  # set the value to "infinity"
			A_	:					Union[str, 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
				A_	:					Tuple						 =		dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
				A_	:					List[str]						 =		dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
				A_	:					Optional[int]						 =		left + total[i][j] + right

				if dp[i][j] > cost:
					A_	:					Dict						 =		cost
					A_	:					List[str]						 =		r

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

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

def 		lowercase_   (		):




	"""simple docstring"""






	A_	:					List[Any]						 =		[Node(_UpperCAmelCase	,   randint(1	,   50						)						) for i in range(10	,   0	,   -1						)]
	find_optimal_binary_search_tree(_UpperCAmelCase						)


if __name__ == "__main__":
		main()





