

'''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						:






			def __init__(   self       ,_snake_case       ,_snake_case			):
				UpperCAmelCase_			:	Dict      =   key
				UpperCAmelCase_			:	Dict      =   freq






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




def       a__    (  _SCREAMING_SNAKE_CASE					:    Optional[Any]     ,							_SCREAMING_SNAKE_CASE					:    Any     ,							_SCREAMING_SNAKE_CASE					:    int     ,							_SCREAMING_SNAKE_CASE					:    Dict     ,							_SCREAMING_SNAKE_CASE					:    Tuple     ,							_SCREAMING_SNAKE_CASE					:    Optional[int]							)			-> str:


	"""simple docstring"""





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

	UpperCAmelCase_			:	Dict      =   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(_SCREAMING_SNAKE_CASE     ,							_SCREAMING_SNAKE_CASE     ,							_SCREAMING_SNAKE_CASE     ,							node - 1     ,							key[node]     ,							_SCREAMING_SNAKE_CASE							)
	print_binary_search_tree(_SCREAMING_SNAKE_CASE     ,							_SCREAMING_SNAKE_CASE     ,							node + 1     ,							_SCREAMING_SNAKE_CASE     ,							key[node]     ,							_SCREAMING_SNAKE_CASE							)


def       a__    (  _SCREAMING_SNAKE_CASE					:    Union[str, Any]							)			-> List[Any]:


	"""simple docstring"""





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

	UpperCAmelCase_			:	Optional[Any]      =   len(_SCREAMING_SNAKE_CASE							)

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

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

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

				if dp[i][j] > cost:
					UpperCAmelCase_			:	List[Any]      =   cost
					UpperCAmelCase_			:	Dict      =   r

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

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


def       a__    (  )			-> Dict:


	"""simple docstring"""





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


if __name__ == "__main__":
					main()







'''simple docstring'''
import gc
import unittest

import numpy as np
import torch

from diffusers import RePaintPipeline, RePaintScheduler, UNetaDModel
from diffusers.utils.testing_utils import (
    enable_full_determinism,
    load_image,
    load_numpy,
    nightly,
    require_torch_gpu,
    skip_mps,
    torch_device,
)

from ..pipeline_params import IMAGE_INPAINTING_BATCH_PARAMS, IMAGE_INPAINTING_PARAMS
from ..test_pipelines_common import PipelineTesterMixin


enable_full_determinism()
class  _snake_case						(__SCREAMING_SNAKE_CASE       ,       unittest.TestCase):
			__A   :     List[str]          =RePaintPipeline
			__A   :     List[str]          =IMAGE_INPAINTING_PARAMS - {"width", "height", "guidance_scale"}
			__A   :     List[Any]          =PipelineTesterMixin.required_optional_params - {
			    "latents",
			    "num_images_per_prompt",
			    "callback",
			    "callback_steps",
			}
			__A   :     str          =IMAGE_INPAINTING_BATCH_PARAMS
			__A   :     Union[str, Any]          =False






			def 						UpperCamelCase__				(   self			):
				torch.manual_seed(0			)
				torch.manual_seed(0			)
				UpperCAmelCase_			:	Union[str, Any]      =   UNetaDModel(
				    block_out_channels=(32, 64)       ,layers_per_block=2       ,sample_size=32       ,in_channels=3       ,out_channels=3       ,down_block_types=("DownBlock2D", "AttnDownBlock2D")       ,up_block_types=("AttnUpBlock2D", "UpBlock2D")       ,)
				UpperCAmelCase_			:	Optional[int]      =   RePaintScheduler()
				UpperCAmelCase_			:	List[Any]      =   {"unet": unet, "scheduler": scheduler}
				return components






			def 						UpperCamelCase__				(   self       ,_snake_case       ,_snake_case=0			):
				if str(_snake_case			).startswith("mps"			):
					UpperCAmelCase_			:	Optional[Any]      =   torch.manual_seed(_snake_case			)
				else:
					UpperCAmelCase_			:	Union[str, Any]      =   torch.Generator(device=_snake_case			).manual_seed(_snake_case			)
				UpperCAmelCase_			:	List[str]      =   np.random.RandomState(_snake_case			).standard_normal((1, 3, 32, 32)			)
				UpperCAmelCase_			:	str      =   torch.from_numpy(_snake_case			).to(device=_snake_case       ,dtype=torch.floataa			)
				UpperCAmelCase_			:	str      =   (image > 0).to(device=_snake_case       ,dtype=torch.floataa			)
				UpperCAmelCase_			:	str      =   {
				    "image": image,
				    "mask_image": mask,
				    "generator": generator,
				    "num_inference_steps": 5,
				    "eta": 0.0,
				    "jump_length": 2,
				    "jump_n_sample": 2,
				    "output_type": "numpy",
				}
				return inputs






			def 						UpperCamelCase__				(   self			):
				UpperCAmelCase_			:	Union[str, Any]      =   "cpu"  # ensure determinism for the device-dependent torch.Generator
				UpperCAmelCase_			:	List[Any]      =   self.get_dummy_components()
				UpperCAmelCase_			:	Union[str, Any]      =   RePaintPipeline(**_snake_case			)
				UpperCAmelCase_			:	Dict      =   sd_pipe.to(_snake_case			)
				sd_pipe.set_progress_bar_config(disable=_snake_case			)

				UpperCAmelCase_			:	Union[str, Any]      =   self.get_dummy_inputs(_snake_case			)
				UpperCAmelCase_			:	Union[str, Any]      =   sd_pipe(**_snake_case			).images
				UpperCAmelCase_			:	Dict      =   image[0, -3:, -3:, -1]

				assert image.shape == (1, 32, 32, 3)
				UpperCAmelCase_			:	List[Any]      =   np.array([1.0000, 0.5426, 0.5497, 0.2200, 1.0000, 1.0000, 0.5623, 1.0000, 0.6274]			)

				assert np.abs(image_slice.flatten() - expected_slice			).max() < 1E-3






			@skip_mps
			def 						UpperCamelCase__				(   self			):
				return super().test_save_load_local()






			@unittest.skip("non-deterministic pipeline"			)
			def 						UpperCamelCase__				(   self			):
				return super().test_inference_batch_single_identical()






			@skip_mps
			def 						UpperCamelCase__				(   self			):
				return super().test_dict_tuple_outputs_equivalent()






			@skip_mps
			def 						UpperCamelCase__				(   self			):
				return super().test_save_load_optional_components()






			@skip_mps
			def 						UpperCamelCase__				(   self			):
				return super().test_attention_slicing_forward_pass()




@nightly
@require_torch_gpu
class  _snake_case						(unittest.TestCase):






			def 						UpperCamelCase__				(   self			):
				super().tearDown()
				gc.collect()
				torch.cuda.empty_cache()






			def 						UpperCamelCase__				(   self			):
				UpperCAmelCase_			:	Union[str, Any]      =   load_image(
				    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/"
				    "repaint/celeba_hq_256.png"			)
				UpperCAmelCase_			:	Any      =   load_image(
				    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/repaint/mask_256.png"			)
				UpperCAmelCase_			:	str      =   load_numpy(
				    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/"
				    "repaint/celeba_hq_256_result.npy"			)

				UpperCAmelCase_			:	Optional[Any]      =   "google/ddpm-ema-celebahq-256"
				UpperCAmelCase_			:	Optional[int]      =   UNetaDModel.from_pretrained(_snake_case			)
				UpperCAmelCase_			:	Optional[int]      =   RePaintScheduler.from_pretrained(_snake_case			)

				UpperCAmelCase_			:	Union[str, Any]      =   RePaintPipeline(unet=_snake_case       ,scheduler=_snake_case			).to(_snake_case			)
				repaint.set_progress_bar_config(disable=_snake_case			)
				repaint.enable_attention_slicing()

				UpperCAmelCase_			:	Any      =   torch.manual_seed(0			)
				UpperCAmelCase_			:	Union[str, Any]      =   repaint(
				    _snake_case       ,_snake_case       ,num_inference_steps=2_50       ,eta=0.0       ,jump_length=10       ,jump_n_sample=10       ,generator=_snake_case       ,output_type="np"       ,)
				UpperCAmelCase_			:	Union[str, Any]      =   output.images[0]

				assert image.shape == (2_56, 2_56, 3)
				assert np.abs(expected_image - image			).mean() < 1E-2




