
'''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__    :







		"""simple docstring"""

		def __init__(	self							:       Tuple   ,     UpperCamelCase__							:       Tuple   ,     UpperCamelCase__							:       Optional[int]	)		->       str:






				"""simple docstring"""







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



		def __str__(	self							:       int	)		->       Dict:






				"""simple docstring"""







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







def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__       )   ->				int:


		'''simple docstring'''


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

		snake_case   :    str			       =		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 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				Optional[Any]:


		'''simple docstring'''


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

		snake_case   :    Union[str, Any]			       =		len(SCREAMING_SNAKE_CASE__       )

		snake_case   :    str			       =		[nodes[i].key for i in range(SCREAMING_SNAKE_CASE__       )]
		snake_case   :    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.
		snake_case   :    List[str]			       =		[[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
		snake_case   :    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
		snake_case   :    Optional[Any]			       =		[[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       ):
						snake_case   :    Any			       =		i + interval_length - 1

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

								if dp[i][j] > cost:
										snake_case   :    Tuple			       =		cost
										snake_case   :    Tuple			       =		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 					_UpperCamelCase		(    )   ->				int:


		'''simple docstring'''


		snake_case   :    Dict			       =		[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 unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin


if is_torch_available():
						import torch

if is_vision_available():
						from PIL import Image

						from transformers import BlipImageProcessor






class      snake_case__    (	unittest.TestCase ):







		"""simple docstring"""

		def __init__(	self							:       List[str]   ,     UpperCamelCase__							:       Union[str, Any]   ,     UpperCamelCase__							:       Optional[Any]=7   ,     UpperCamelCase__							:       Union[str, Any]=3   ,     UpperCamelCase__							:       Tuple=18   ,     UpperCamelCase__							:       Union[str, Any]=30   ,     UpperCamelCase__							:       Dict=400   ,     UpperCamelCase__							:       Tuple=True   ,     UpperCamelCase__							:       Optional[Any]=None   ,     UpperCamelCase__							:       Any=True   ,     UpperCamelCase__							:       Dict=False   ,     UpperCamelCase__							:       Dict=[0.48_145_466, 0.4_578_275, 0.40_821_073]   ,     UpperCamelCase__							:       int=[0.26_862_954, 0.26_130_258, 0.27_577_711]   ,     UpperCamelCase__							:       str=True   ,     )		->       Any:






				"""simple docstring"""







				snake_case   :    Dict			       =		size if size is not None else {'''height''': 20, '''width''': 20}
				snake_case   :    Union[str, Any]			       =		parent
				snake_case   :    Optional[int]			       =		batch_size
				snake_case   :    Dict			       =		num_channels
				snake_case   :    List[Any]			       =		image_size
				snake_case   :    List[Any]			       =		min_resolution
				snake_case   :    Dict			       =		max_resolution
				snake_case   :    Dict			       =		do_resize
				snake_case   :    Optional[int]			       =		size
				snake_case   :    Dict			       =		do_normalize
				snake_case   :    Tuple			       =		image_mean
				snake_case   :    Optional[int]			       =		image_std
				snake_case   :    int			       =		do_pad
				snake_case   :    List[Any]			       =		do_convert_rgb



		def 	lowerCAmelCase							(	self							:       str	)		->       Optional[int]:






				"""simple docstring"""







				return {
				    "do_resize": self.do_resize,
				    "size": self.size,
				    "do_normalize": self.do_normalize,
				    "image_mean": self.image_mean,
				    "image_std": self.image_std,
				    "do_convert_rgb": self.do_convert_rgb,
				    "do_pad": self.do_pad,
				}



		def 	lowerCAmelCase							(	self							:       str   ,     UpperCamelCase__							:       Optional[int]=False   ,     UpperCamelCase__							:       Tuple=False   ,     UpperCamelCase__							:       Union[str, Any]=False	)		->       List[str]:






				"""simple docstring"""







				assert not (numpify and torchify), "You cannot specify both numpy and PyTorch tensors at the same time"

				if equal_resolution:
						snake_case   :    Any			       =		[]
						for i in range(self.batch_size	):
								image_inputs.append(
								    np.random.randint(
								        255   ,     size=(self.num_channels, self.max_resolution, self.max_resolution)   ,     dtype=np.uinta	)	)
				else:
						snake_case   :    Union[str, Any]			       =		[]
						for i in range(self.batch_size	):
								snake_case       ,snake_case   :    List[Any]			       =		np.random.choice(np.arange(self.min_resolution   ,     self.max_resolution	)   ,     2	)
								image_inputs.append(np.random.randint(255   ,     size=(self.num_channels, width, height)   ,     dtype=np.uinta	)	)

				if not numpify and not torchify:
						# PIL expects the channel dimension as last dimension
						snake_case   :    Optional[int]			       =		[Image.fromarray(np.moveaxis(UpperCamelCase__   ,     0   ,     -1	)	) for x in image_inputs]

				if torchify:
						snake_case   :    Optional[Any]			       =		[torch.from_numpy(UpperCamelCase__	) for x in image_inputs]

				return image_inputs







@require_torch
@require_vision
class      snake_case__    (	__SCREAMING_SNAKE_CASE  , unittest.TestCase ):







		"""simple docstring"""

		lowerCamelCase							=		BlipImageProcessor if is_vision_available() else None



		def 	lowerCAmelCase							(	self							:       Dict	)		->       Optional[int]:






				"""simple docstring"""







				snake_case   :    Union[str, Any]			       =		BlipImageProcessingTester(self	)



		@property
		def 	lowerCAmelCase							(	self							:       Any	)		->       Union[str, Any]:






				"""simple docstring"""







				return self.image_processor_tester.prepare_image_processor_dict()



		def 	lowerCAmelCase							(	self							:       Optional[Any]	)		->       Any:






				"""simple docstring"""







				snake_case   :    Dict			       =		self.image_processing_class(**self.image_processor_dict	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_resize'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''size'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_normalize'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''image_mean'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''image_std'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_convert_rgb'''	)	)



		def 	lowerCAmelCase							(	self							:       Any	)		->       Dict:






				"""simple docstring"""







				pass



		def 	lowerCAmelCase							(	self							:       List[str]	)		->       Tuple:






				"""simple docstring"""







				snake_case   :    Optional[Any]			       =		self.image_processing_class(**self.image_processor_dict	)
				# create random PIL images
				snake_case   :    Union[str, Any]			       =		self.image_processor_tester.prepare_inputs(equal_resolution=UpperCamelCase__	)
				for image in image_inputs:
						self.assertIsInstance(UpperCamelCase__   ,     Image.Image	)

				# Test not batched input
				snake_case   :    Optional[int]			       =		image_processor(image_inputs[0]   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        1,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )

				# Test batched
				snake_case   :    int			       =		image_processor(UpperCamelCase__   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )



		def 	lowerCAmelCase							(	self							:       List[str]	)		->       Tuple:






				"""simple docstring"""







				snake_case   :    Any			       =		self.image_processing_class(**self.image_processor_dict	)
				# create random numpy tensors
				snake_case   :    List[str]			       =		self.image_processor_tester.prepare_inputs(equal_resolution=UpperCamelCase__   ,     numpify=UpperCamelCase__	)
				for image in image_inputs:
						self.assertIsInstance(UpperCamelCase__   ,     np.ndarray	)

				# Test not batched input
				snake_case   :    Dict			       =		image_processor(image_inputs[0]   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        1,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )

				# Test batched
				snake_case   :    Dict			       =		image_processor(UpperCamelCase__   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )



		def 	lowerCAmelCase							(	self							:       Dict	)		->       Union[str, Any]:






				"""simple docstring"""







				snake_case   :    Union[str, Any]			       =		self.image_processing_class(**self.image_processor_dict	)
				# create random PyTorch tensors
				snake_case   :    List[Any]			       =		self.image_processor_tester.prepare_inputs(equal_resolution=UpperCamelCase__   ,     torchify=UpperCamelCase__	)
				for image in image_inputs:
						self.assertIsInstance(UpperCamelCase__   ,     torch.Tensor	)

				# Test not batched input
				snake_case   :    List[str]			       =		image_processor(image_inputs[0]   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        1,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )

				# Test batched
				snake_case   :    str			       =		image_processor(UpperCamelCase__   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )







@require_torch
@require_vision
class      snake_case__    (	__SCREAMING_SNAKE_CASE  , unittest.TestCase ):







		"""simple docstring"""

		lowerCamelCase							=		BlipImageProcessor if is_vision_available() else None



		def 	lowerCAmelCase							(	self							:       Tuple	)		->       Union[str, Any]:






				"""simple docstring"""







				snake_case   :    Union[str, Any]			       =		BlipImageProcessingTester(self   ,     num_channels=4	)
				snake_case   :    Optional[int]			       =		3



		@property
		def 	lowerCAmelCase							(	self							:       Optional[int]	)		->       Tuple:






				"""simple docstring"""







				return self.image_processor_tester.prepare_image_processor_dict()



		def 	lowerCAmelCase							(	self							:       List[Any]	)		->       Any:






				"""simple docstring"""







				snake_case   :    Union[str, Any]			       =		self.image_processing_class(**self.image_processor_dict	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_resize'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''size'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_normalize'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''image_mean'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''image_std'''	)	)
				self.assertTrue(hasattr(UpperCamelCase__   ,     '''do_convert_rgb'''	)	)



		def 	lowerCAmelCase							(	self							:       Optional[Any]	)		->       List[str]:






				"""simple docstring"""







				pass



		def 	lowerCAmelCase							(	self							:       Optional[int]	)		->       Any:






				"""simple docstring"""







				snake_case   :    Optional[Any]			       =		self.image_processing_class(**self.image_processor_dict	)
				# create random PIL images
				snake_case   :    Tuple			       =		self.image_processor_tester.prepare_inputs(equal_resolution=UpperCamelCase__	)
				for image in image_inputs:
						self.assertIsInstance(UpperCamelCase__   ,     Image.Image	)

				# Test not batched input
				snake_case   :    int			       =		image_processor(image_inputs[0]   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        1,
				        self.expected_encoded_image_num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )

				# Test batched
				snake_case   :    Union[str, Any]			       =		image_processor(UpperCamelCase__   ,     return_tensors='''pt'''	).pixel_values
				self.assertEqual(
				    encoded_images.shape   ,     (
				        self.image_processor_tester.batch_size,
				        self.expected_encoded_image_num_channels,
				        self.image_processor_tester.size['''height'''],
				        self.image_processor_tester.size['''width'''],
				    )   ,     )


