code: 
  """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 A_			:
  
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
  
    def __init__(	self       ,     lowercase_       ,     lowercase_						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[int]      =					key
       UpperCAmelCase_      :      Any      =					freq
  
  
  
  
  
  
  
    def __str__(	self						):
  
       """simple docstring"""
       return F"""Node(key={self.key}, freq={self.freq})"""
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase,	__lowerCamelCase						):
     if i > j or i < 0 or j > len(snake_case__						) - 1:
        return
  
     UpperCAmelCase_      :      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(snake_case__,	snake_case__,	snake_case__,	node - 1,	key[node],	snake_case__						)
     print_binary_search_tree(snake_case__,	snake_case__,	node + 1,	snake_case__,	key[node],	snake_case__						)
  
  
  
  
  
  
  
  def 			__a  (	__lowerCamelCase						):
     nodes.sort(key=lambda __lowerCamelCase						: node.key						)
  
     UpperCAmelCase_      :      Optional[Any]      =					len(snake_case__						)
  
     UpperCAmelCase_      :      int      =					[nodes[i].key for i in range(snake_case__						)]
     UpperCAmelCase_      :      Union[str, Any]      =					[nodes[i].freq for i in range(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_      :      Tuple      =					[[freqs[i] if i == j else 0 for j in range(snake_case__						)] for i in range(snake_case__						)]
     # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
     # array
     UpperCAmelCase_      :      List[str]      =					[[freqs[i] if i == j else 0 for j in range(snake_case__						)] for i in range(snake_case__						)]
     # stores tree roots that will be used later for constructing binary search tree
     UpperCAmelCase_      :      Optional[Any]      =					[[i if i == j else 0 for j in range(snake_case__						)] for i in range(snake_case__						)]
  
     for interval_length in range(2,	n + 1						):
        for i in range(n - interval_length + 1						):
           UpperCAmelCase_      :      Union[str, Any]      =					i + interval_length - 1
  
           UpperCAmelCase_      :      Dict      =					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_      :      Optional[Any]      =					dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
              UpperCAmelCase_      :      List[str]      =					dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
              UpperCAmelCase_      :      Optional[Any]      =					left + total[i][j] + right
  
              if dp[i][j] > cost:
                 UpperCAmelCase_      :      Tuple      =					cost
                 UpperCAmelCase_      :      Optional[int]      =					r
  
     print("Binary search tree nodes:"						)
     for node in nodes:
        print(snake_case__						)
  
     print(f"""\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}."""						)
     print_binary_search_tree(snake_case__,	snake_case__,	0,	n - 1,	-1,	snake_case__						)
  
  
  
  
  
  
  
  def 			__a  (	):
     # A sample binary search tree
     UpperCAmelCase_      :      Dict      =					[Node(snake_case__,	randint(1,	50						)						) for i in range(10,	0,	-1						)]
     find_optimal_binary_search_tree(snake_case__						)
  
  
  if __name__ == "__main__":
      main()
  
style_context: 
  """simple docstring"""
  
  
  
  
  
  import shutil
  import tempfile
  import unittest
  
  import numpy as np
  import pytest
  
  from transformers.testing_utils import require_vision
  from transformers.utils import is_vision_available
  
  
  if is_vision_available():
      from PIL import Image
  
      from transformers import AutoProcessor, BertTokenizer, CLIPImageProcessor, GitProcessor, PreTrainedTokenizerFast
  
  
  @require_vision
  class A_			(unittest.TestCase   ):
  
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[int]      =					tempfile.mkdtemp()
  
       UpperCAmelCase_      :      List[Any]      =					CLIPImageProcessor()
       UpperCAmelCase_      :      Any      =					BertTokenizer.from_pretrained(
           "hf-internal-testing/tiny-random-BertModel"       ,     model_input_names=["input_ids", "attention_mask"]						)
  
       UpperCAmelCase_      :      Tuple      =					GitProcessor(lowercase_       ,     lowercase_						)
  
       processor.save_pretrained(self.tmpdirname						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self       ,     **lowercase_						):
  
       """simple docstring"""
       return AutoProcessor.from_pretrained(self.tmpdirname       ,     **lowercase_						).tokenizer
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self       ,     **lowercase_						):
  
       """simple docstring"""
       return AutoProcessor.from_pretrained(self.tmpdirname       ,     **lowercase_						).image_processor
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       shutil.rmtree(self.tmpdirname						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[int]      =					[np.random.randint(255       ,     size=(3, 30, 400)       ,     dtype=np.uinta						)]
  
       UpperCAmelCase_      :      Optional[Any]      =					[Image.fromarray(np.moveaxis(lowercase_       ,     0       ,     -1						)						) for x in image_inputs]
  
       return image_inputs
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      List[Any]      =					GitProcessor(tokenizer=self.get_tokenizer()       ,     image_processor=self.get_image_processor()						)
       processor.save_pretrained(self.tmpdirname						)
  
       UpperCAmelCase_      :      Optional[int]      =					self.get_tokenizer(bos_token="(BOS)"       ,     eos_token="(EOS)"						)
       UpperCAmelCase_      :      Union[str, Any]      =					self.get_image_processor(do_normalize=lowercase_       ,     padding_value=1.0						)
  
       UpperCAmelCase_      :      str      =					GitProcessor.from_pretrained(
           self.tmpdirname       ,     bos_token="(BOS)"       ,     eos_token="(EOS)"       ,     do_normalize=lowercase_       ,     padding_value=1.0						)
  
       self.assertEqual(processor.tokenizer.get_vocab()       ,     tokenizer_add_kwargs.get_vocab()						)
       self.assertIsInstance(processor.tokenizer       ,     lowercase_						)
  
       self.assertEqual(processor.image_processor.to_json_string()       ,     image_processor_add_kwargs.to_json_string()						)
       self.assertIsInstance(processor.image_processor       ,     lowercase_						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Dict      =					self.get_image_processor()
       UpperCAmelCase_      :      Union[str, Any]      =					self.get_tokenizer()
  
       UpperCAmelCase_      :      Union[str, Any]      =					GitProcessor(tokenizer=lowercase_       ,     image_processor=lowercase_						)
  
       UpperCAmelCase_      :      List[Any]      =					self.prepare_image_inputs()
  
       UpperCAmelCase_      :      Optional[Any]      =					image_processor(lowercase_       ,     return_tensors="np"						)
       UpperCAmelCase_      :      int      =					processor(images=lowercase_       ,     return_tensors="np"						)
  
       for key in input_feat_extract.keys():
          self.assertAlmostEqual(input_feat_extract[key].sum()       ,     input_processor[key].sum()       ,     delta=1E-2						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Union[str, Any]      =					self.get_image_processor()
       UpperCAmelCase_      :      Tuple      =					self.get_tokenizer()
  
       UpperCAmelCase_      :      int      =					GitProcessor(tokenizer=lowercase_       ,     image_processor=lowercase_						)
  
       UpperCAmelCase_      :      Optional[Any]      =					"lower newer"
  
       UpperCAmelCase_      :      Any      =					processor(text=lowercase_						)
  
       UpperCAmelCase_      :      int      =					tokenizer(lowercase_       ,     return_token_type_ids=lowercase_						)
  
       for key in encoded_tok.keys():
          self.assertListEqual(encoded_tok[key]       ,     encoded_processor[key]						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[int]      =					self.get_image_processor()
       UpperCAmelCase_      :      Union[str, Any]      =					self.get_tokenizer()
  
       UpperCAmelCase_      :      Optional[int]      =					GitProcessor(tokenizer=lowercase_       ,     image_processor=lowercase_						)
  
       UpperCAmelCase_      :      List[str]      =					"lower newer"
       UpperCAmelCase_      :      Dict      =					self.prepare_image_inputs()
  
       UpperCAmelCase_      :      Any      =					processor(text=lowercase_       ,     images=lowercase_						)
  
       self.assertListEqual(list(inputs.keys()						)       ,     ["input_ids", "attention_mask", "pixel_values"]						)
  
       # test if it raises when no input is passed
       with pytest.raises(lowercase_						):
          processor()
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Optional[Any]      =					self.get_image_processor()
       UpperCAmelCase_      :      str      =					self.get_tokenizer()
  
       UpperCAmelCase_      :      int      =					GitProcessor(tokenizer=lowercase_       ,     image_processor=lowercase_						)
  
       UpperCAmelCase_      :      Tuple      =					[[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]
  
       UpperCAmelCase_      :      Any      =					processor.batch_decode(lowercase_						)
       UpperCAmelCase_      :      Optional[Any]      =					tokenizer.batch_decode(lowercase_						)
  
       self.assertListEqual(lowercase_       ,     lowercase_						)
  
  
  
  
  
  
  
    def  UpperCamelCase__      (	self						):
  
       """simple docstring"""
       UpperCAmelCase_      :      Union[str, Any]      =					self.get_image_processor()
       UpperCAmelCase_      :      Optional[Any]      =					self.get_tokenizer()
  
       UpperCAmelCase_      :      str      =					GitProcessor(tokenizer=lowercase_       ,     image_processor=lowercase_						)
  
       UpperCAmelCase_      :      int      =					"lower newer"
       UpperCAmelCase_      :      Tuple      =					self.prepare_image_inputs()
  
       UpperCAmelCase_      :      Optional[Any]      =					processor(text=lowercase_       ,     images=lowercase_						)
  
       # For now the processor supports only ['input_ids', 'attention_mask', 'pixel_values']
       self.assertListEqual(list(inputs.keys()						)       ,     ["input_ids", "attention_mask", "pixel_values"]						)
  
  
  