code: 
  
  # 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     lowerCamelCase_			:
  
  
  
  
  	def __init__(    self	:    Dict				,			__A	:    int				,			__A	:    List[str]       ):
  		__A   : Optional[int]								= key
  		__A   : Optional[int]								= freq
  
  
  
  
  	def __str__(    self	:    Optional[int]       ):
  		return F"""Node(key={self.key}, freq={self.freq})"""
  
  
  
  
  
  
  def        __SCREAMING_SNAKE_CASE    (      a__						:      Tuple ,a__						:      Union[str, Any] ,a__						:      Optional[Any] ,a__						:      Tuple ,a__						:      Tuple ,a__						:      List[Any]					)				->							Tuple:
  	if i > j or i < 0 or j > len(a__					) - 1:
  		return
  
  	__A   : Optional[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(a__ ,a__ ,a__ ,node - 1 ,key[node] ,a__					)
  	print_binary_search_tree(a__ ,a__ ,node + 1 ,a__ ,key[node] ,a__					)
  def        __SCREAMING_SNAKE_CASE    (      a__						:      str					)				->							Union[str, Any]:
  	nodes.sort(key=lambda a__					: node.key					)
  
  	__A   : Optional[int]								= len(a__					)
  
  	__A   : List[str]								= [nodes[i].key for i in range(a__					)]
  	__A   : List[Any]								= [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   : Tuple								= [[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   : Any								= [[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   : str								= [[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   : Any								= i + interval_length - 1
  
  			__A   : Optional[int]								= sys.maxsize  # set the value to "infinity"
  			__A   : Dict								= 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   : List[str]								= dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
  				__A   : str								= dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
  				__A   : Tuple								= left + total[i][j] + right
  
  				if dp[i][j] > cost:
  					__A   : str								= cost
  					__A   : Any								= 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        __SCREAMING_SNAKE_CASE    (      )				->							List[str]:
  	# A sample binary search tree
  	__A   : Optional[int]								= [Node(a__ ,randint(1 ,50					)					) for i in range(10 ,0 ,-1					)]
  	find_optimal_binary_search_tree(a__					)
  
  
  if __name__ == "__main__":
  			main()
  
  
  
  
  
  
style_context: 
  
  import unittest
  from pathlib import Path
  
  from transformers import is_vision_available, load_tool
  from transformers.testing_utils import get_tests_dir
  
  from .test_tools_common import ToolTesterMixin
  
  
  if is_vision_available():
  			from PIL import Image
  
  
  
  
  
  
  class     lowerCamelCase_			(  unittest.TestCase	,			_lowercase  ):
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Dict       ):
  		__A   : str								= load_tool("""image-captioning"""       )
  		self.tool.setup()
  		__A   : Dict								= load_tool("""image-captioning"""				,			remote=__A       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Optional[int]       ):
  		__A   : List[Any]								= Image.open(Path(get_tests_dir("""fixtures/tests_samples/COCO"""       )       ) / """000000039769.png"""       )
  		__A   : Optional[Any]								= self.tool(__A       )
  		self.assertEqual(__A				,			"""two cats sleeping on a couch"""       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Dict       ):
  		__A   : Any								= Image.open(Path(get_tests_dir("""fixtures/tests_samples/COCO"""       )       ) / """000000039769.png"""       )
  		__A   : List[str]								= self.remote_tool(__A       )
  		self.assertEqual(__A				,			"""two cats sleeping on a couch"""       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Union[str, Any]       ):
  		__A   : Optional[Any]								= Image.open(Path(get_tests_dir("""fixtures/tests_samples/COCO"""       )       ) / """000000039769.png"""       )
  		__A   : str								= self.tool(image=__A       )
  		self.assertEqual(__A				,			"""two cats sleeping on a couch"""       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    str       ):
  		__A   : Dict								= Image.open(Path(get_tests_dir("""fixtures/tests_samples/COCO"""       )       ) / """000000039769.png"""       )
  		__A   : List[Any]								= self.remote_tool(image=__A       )
  		self.assertEqual(__A				,			"""two cats sleeping on a couch"""       )
  
  
  
  
  
  