
# 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 	A_       :




	'''simple docstring'''


	def __init__(	self		,   snake_case		,   snake_case	):
		lowercase					  =   key
		lowercase					  =   freq





	def __str__(	self	):
		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							):
	if i > j or i < 0 or j > len(__SCREAMING_SNAKE_CASE							) - 1:
		return

	lowercase					  =   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							):
	nodes.sort(key=lambda __SCREAMING_SNAKE_CASE							: node.key							)

	lowercase					  =   len(__SCREAMING_SNAKE_CASE							)

	lowercase					  =   [nodes[i].key for i in range(__SCREAMING_SNAKE_CASE							)]
	lowercase					  =   [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.
	lowercase					  =   [[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
	lowercase					  =   [[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
	lowercase					  =   [[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							):
			lowercase					  =   i + interval_length - 1

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

				if dp[i][j] > cost:
					lowercase					  =   cost
					lowercase					  =   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_		(							):
	# A sample binary search tree
	lowercase					  =   [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()



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, prepare_video_inputs


if is_torch_available():
	import torch

if is_vision_available():
	from PIL import Image

	from transformers import VideoMAEImageProcessor







class 	A_       (      unittest.TestCase       ):




	'''simple docstring'''


	def __init__(	self		,   snake_case		,   snake_case=7		,   snake_case=3		,   snake_case=10		,   snake_case=18		,   snake_case=30		,   snake_case=400		,   snake_case=True		,   snake_case=None		,   snake_case=True		,   snake_case=[0.5, 0.5, 0.5]		,   snake_case=[0.5, 0.5, 0.5]		,   snake_case=None		,   ):
		lowercase					  =   size if size is not None else {'shortest_edge': 18}
		lowercase					  =   crop_size if crop_size is not None else {'height': 18, 'width': 18}

		lowercase					  =   parent
		lowercase					  =   batch_size
		lowercase					  =   num_channels
		lowercase					  =   num_frames
		lowercase					  =   image_size
		lowercase					  =   min_resolution
		lowercase					  =   max_resolution
		lowercase					  =   do_resize
		lowercase					  =   size
		lowercase					  =   do_normalize
		lowercase					  =   image_mean
		lowercase					  =   image_std
		lowercase					  =   crop_size





	def      SCREAMING_SNAKE_CASE__						(	self	):
		return {
		    "image_mean": self.image_mean,
		    "image_std": self.image_std,
		    "do_normalize": self.do_normalize,
		    "do_resize": self.do_resize,
		    "size": self.size,
		    "crop_size": self.crop_size,
		}







@require_torch
@require_vision
class 	A_       (      __lowerCamelCase				,     unittest.TestCase       ):




	'''simple docstring'''


	_UpperCamelCase					:					List[str]										=	VideoMAEImageProcessor if is_vision_available() else None





	def      SCREAMING_SNAKE_CASE__						(	self	):
		lowercase					  =   VideoMAEImageProcessingTester(self	)





	@property
	def      SCREAMING_SNAKE_CASE__						(	self	):
		return self.image_processor_tester.prepare_image_processor_dict()





	def      SCREAMING_SNAKE_CASE__						(	self	):
		lowercase					  =   self.image_processing_class(**self.image_processor_dict	)
		self.assertTrue(hasattr(snake_case		,   'image_mean'	)	)
		self.assertTrue(hasattr(snake_case		,   'image_std'	)	)
		self.assertTrue(hasattr(snake_case		,   'do_normalize'	)	)
		self.assertTrue(hasattr(snake_case		,   'do_resize'	)	)
		self.assertTrue(hasattr(snake_case		,   'do_center_crop'	)	)
		self.assertTrue(hasattr(snake_case		,   'size'	)	)





	def      SCREAMING_SNAKE_CASE__						(	self	):
		lowercase					  =   self.image_processing_class.from_dict(self.image_processor_dict	)
		self.assertEqual(image_processor.size		,   {'shortest_edge': 18}	)
		self.assertEqual(image_processor.crop_size		,   {'height': 18, 'width': 18}	)

		lowercase					  =   self.image_processing_class.from_dict(self.image_processor_dict		,   size=42		,   crop_size=84	)
		self.assertEqual(image_processor.size		,   {'shortest_edge': 42}	)
		self.assertEqual(image_processor.crop_size		,   {'height': 84, 'width': 84}	)





	def      SCREAMING_SNAKE_CASE__						(	self	):
		pass





	def      SCREAMING_SNAKE_CASE__						(	self	):
		# Initialize image_processing
		lowercase					  =   self.image_processing_class(**self.image_processor_dict	)
		# create random PIL videos
		lowercase					  =   prepare_video_inputs(self.image_processor_tester		,   equal_resolution=snake_case	)
		for video in video_inputs:
			self.assertIsInstance(snake_case		,   snake_case	)
			self.assertIsInstance(video[0]		,   Image.Image	)

		# Test not batched input
		lowercase					  =   image_processing(video_inputs[0]		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        1,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )

		# Test batched
		lowercase					  =   image_processing(snake_case		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        self.image_processor_tester.batch_size,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )





	def      SCREAMING_SNAKE_CASE__						(	self	):
		# Initialize image_processing
		lowercase					  =   self.image_processing_class(**self.image_processor_dict	)
		# create random numpy tensors
		lowercase					  =   prepare_video_inputs(self.image_processor_tester		,   equal_resolution=snake_case		,   numpify=snake_case	)
		for video in video_inputs:
			self.assertIsInstance(snake_case		,   snake_case	)
			self.assertIsInstance(video[0]		,   np.ndarray	)

		# Test not batched input
		lowercase					  =   image_processing(video_inputs[0]		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        1,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )

		# Test batched
		lowercase					  =   image_processing(snake_case		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        self.image_processor_tester.batch_size,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )





	def      SCREAMING_SNAKE_CASE__						(	self	):
		# Initialize image_processing
		lowercase					  =   self.image_processing_class(**self.image_processor_dict	)
		# create random PyTorch tensors
		lowercase					  =   prepare_video_inputs(self.image_processor_tester		,   equal_resolution=snake_case		,   torchify=snake_case	)
		for video in video_inputs:
			self.assertIsInstance(snake_case		,   snake_case	)
			self.assertIsInstance(video[0]		,   torch.Tensor	)

		# Test not batched input
		lowercase					  =   image_processing(video_inputs[0]		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        1,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )

		# Test batched
		lowercase					  =   image_processing(snake_case		,   return_tensors='pt'	).pixel_values
		self.assertEqual(
		    encoded_videos.shape		,   (
		        self.image_processor_tester.batch_size,
		        self.image_processor_tester.num_frames,
		        self.image_processor_tester.num_channels,
		        self.image_processor_tester.crop_size['height'],
		        self.image_processor_tester.crop_size['width'],
		    )		,   )

