




# 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							:	Optional[int]   , __lowerCamelCase							:	Dict   , __lowerCamelCase							:	List[Any]				)   ->	str:
							a       =     key
							a       =     freq





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




def      __magic_name__							(					A						:   int,    A						:   Tuple,    A						:   Tuple,    A						:   Union[str, Any],    A						:   Union[str, Any],    A						:   List[str]  ):






			'''simple docstring'''







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

			a       =     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(A,    A,    A,    node - 1,    key[node],    A  )
			print_binary_search_tree(A,    A,    node + 1,    A,    key[node],    A  )




def      __magic_name__							(					A						:   Any  ):






			'''simple docstring'''







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

			a       =     len(A  )

			a       =     [nodes[i].key for i in range(A  )]
			a       =     [nodes[i].freq for i in range(A  )]

			# 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       =     [[freqs[i] if i == j else 0 for j in range(A  )] for i in range(A  )]
			# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
			# array
			a       =     [[freqs[i] if i == j else 0 for j in range(A  )] for i in range(A  )]
			# stores tree roots that will be used later for constructing binary search tree
			a       =     [[i if i == j else 0 for j in range(A  )] for i in range(A  )]

			for interval_length in range(2,    n + 1  ):
						for i in range(n - interval_length + 1  ):
									a       =     i + interval_length - 1

									a       =     sys.maxsize  # set the value to "infinity"
									a       =     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       =     dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
												a       =     dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
												a       =     left + total[i][j] + right

												if dp[i][j] > cost:
															a       =     cost
															a       =     r

			print("Binary search tree nodes:"  )
			for node in nodes:
						print(A  )

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




def      __magic_name__							(					):






			'''simple docstring'''







			a       =     [Node(A,    randint(1,    50  )  ) for i in range(10,    0,    -1  )]
			find_optimal_binary_search_tree(A  )


if __name__ == "__main__":
		main()












import tempfile
import unittest

import torch

from diffusers import UNetaDConditionModel
from diffusers.training_utils import EMAModel
from diffusers.utils.testing_utils import enable_full_determinism, skip_mps, torch_device


enable_full_determinism()




class        snake_case__				(unittest.TestCase  ):
				"""simple docstring"""



				SCREAMING_SNAKE_CASE_			:				Optional[int]									=   """hf-internal-testing/tiny-stable-diffusion-pipe"""
				SCREAMING_SNAKE_CASE_			:				str									=   1
				SCREAMING_SNAKE_CASE_			:				Dict									=   77
				SCREAMING_SNAKE_CASE_			:				List[str]									=   32
				SCREAMING_SNAKE_CASE_			:				List[str]									=   4
				SCREAMING_SNAKE_CASE_			:				Union[str, Any]									=   64
				SCREAMING_SNAKE_CASE_			:				int									=   torch.manual_seed(0  )





				def 				__UpperCAmelCase				( self							:	List[Any]   , __lowerCamelCase							:	List[Any]=0.9_999				)   ->	Tuple:
							a       =     UNetaDConditionModel.from_pretrained(self.model_id   , subfolder="unet"				)
							a       =     unet.to(__lowerCamelCase				)
							a       =     EMAModel(unet.parameters()   , decay=__lowerCamelCase   , model_cls=__lowerCamelCase   , model_config=unet.config				)
							return unet, ema_unet





				def 				__UpperCAmelCase				( self							:	Tuple				)   ->	Any:
							a       =     torch.randn(
							    self.batch_size   , self.num_in_channels   , self.latent_height   , self.latent_width   , generator=self.generator				).to(__lowerCamelCase				)
							a       =     torch.randint(0   , 10_00   , size=(self.batch_size,)   , generator=self.generator				).to(__lowerCamelCase				)
							a       =     torch.randn(
							    self.batch_size   , self.prompt_length   , self.text_encoder_hidden_dim   , generator=self.generator				).to(__lowerCamelCase				)
							return noisy_latents, timesteps, encoder_hidden_states





				def 				__UpperCAmelCase				( self							:	Optional[int]   , __lowerCamelCase							:	Any				)   ->	Optional[int]:
							a       =     {}
							for k, param in unet.state_dict().items():
										a       =     torch.randn_like(__lowerCamelCase				) + (param * torch.randn_like(__lowerCamelCase				))
										updated_state_dict.update({k: updated_param}				)
							unet.load_state_dict(__lowerCamelCase				)
							return unet





				def 				__UpperCAmelCase				( self							:	Optional[Any]				)   ->	Union[str, Any]:
							a       ,						a       =     self.get_models()
							# Take the first (hypothetical) EMA step.
							ema_unet.step(unet.parameters()				)
							assert ema_unet.optimization_step == 1

							# Take two more.
							for _ in range(2				):
										ema_unet.step(unet.parameters()				)
							assert ema_unet.optimization_step == 3





				def 				__UpperCAmelCase				( self							:	Optional[int]				)   ->	Optional[int]:
							a       ,						a       =     self.get_models()
							# Since the `unet` is not being updated (i.e., backprop'd)
							# there won't be any difference between the `params` of `unet`
							# and `ema_unet` even if we call `ema_unet.step(unet.parameters())`.
							ema_unet.step(unet.parameters()				)
							a       =     list(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)

							# The above holds true even if we call `ema.step()` multiple times since
							# `unet` params are still not being updated.
							for _ in range(4				):
										ema_unet.step(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Any				)   ->	Dict:
							a       ,						a       =     self.get_models()
							# Here we simulate the parameter updates for `unet`. Since there might
							# be some parameters which are initialized to zero we take extra care to
							# initialize their values to something non-zero before the multiplication.
							a       =     self.simulate_backprop(__lowerCamelCase				)

							# Take the EMA step.
							ema_unet.step(unet_pseudo_updated_step_one.parameters()				)

							# Now the EMA'd parameters won't be equal to the original model parameters.
							a       =     list(unet_pseudo_updated_step_one.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)

							# Ensure this is the case when we take multiple EMA steps.
							for _ in range(4				):
										ema_unet.step(unet.parameters()				)
							for s_param, param in zip(ema_unet.shadow_params   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Optional[Any]				)   ->	Any:
							# If we call EMA step after a backpropagation consecutively for two times,
							# the shadow params from those two steps should be different.
							a       ,						a       =     self.get_models()

							# First backprop + EMA
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_one.parameters()				)
							a       =     ema_unet.shadow_params

							# Second backprop + EMA
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_two.parameters()				)
							a       =     ema_unet.shadow_params

							for step_one, step_two in zip(__lowerCamelCase   , __lowerCamelCase				):
										assert ~torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				def 				__UpperCAmelCase				( self							:	Any				)   ->	List[Any]:
							# If there's no decay even if there are backprops, EMA steps
							# won't take any effect i.e., the shadow params would remain the
							# same.
							a       ,						a       =     self.get_models(decay=0.0				)
							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_one.parameters()				)
							a       =     ema_unet.shadow_params

							a       =     self.simulate_backprop(__lowerCamelCase				)
							ema_unet.step(unet_step_two.parameters()				)
							a       =     ema_unet.shadow_params

							for step_one, step_two in zip(__lowerCamelCase   , __lowerCamelCase				):
										assert torch.allclose(__lowerCamelCase   , __lowerCamelCase				)





				@skip_mps
				def 				__UpperCAmelCase				( self							:	List[str]				)   ->	Dict:
							a       ,						a       =     self.get_models()
							a       ,						a       ,						a       =     self.get_dummy_inputs()

							with tempfile.TemporaryDirectory() as tmpdir:
										ema_unet.save_pretrained(__lowerCamelCase				)
										a       =     UNetaDConditionModel.from_pretrained(__lowerCamelCase   , model_cls=__lowerCamelCase				)
										a       =     loaded_unet.to(unet.device				)

							# Since no EMA step has been performed the outputs should match.
							a       =     unet(__lowerCamelCase   , __lowerCamelCase   , __lowerCamelCase				).sample
							a       =     loaded_unet(__lowerCamelCase   , __lowerCamelCase   , __lowerCamelCase				).sample

							assert torch.allclose(__lowerCamelCase   , __lowerCamelCase   , atol=1e-4				)






