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    _lowerCAmelCase						:
  
  
  
  							def __init__(      self ,						a_ ,						a_   )							->							Any:
  								_UpperCAmelCase =						key
  								_UpperCAmelCase =						freq
  
  
  
  							def __str__(      self   )							->							Union[str, Any]:
  								return f"Node(key={self.key}, freq={self.freq})"
  
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if i > j or i < 0 or j > len(UpperCamelCase__      ) - 1:
  		return
  
  	_UpperCAmelCase =						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(UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__				,     node - 1				,     key[node]				,     UpperCamelCase__      )
  	print_binary_search_tree(UpperCamelCase__				,     UpperCamelCase__				,     node + 1				,     UpperCamelCase__				,     key[node]				,     UpperCamelCase__      )
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	nodes.sort(key=lambda UpperCamelCase__      : node.key      )
  
  	_UpperCAmelCase =						len(UpperCamelCase__      )
  
  	_UpperCAmelCase =						[nodes[i].key for i in range(UpperCamelCase__      )]
  	_UpperCAmelCase =						[nodes[i].freq for i in range(UpperCamelCase__      )]
  
  	# 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 =						[[freqs[i] if i == j else 0 for j in range(UpperCamelCase__      )] for i in range(UpperCamelCase__      )]
  	# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
  	# array
  	_UpperCAmelCase =						[[freqs[i] if i == j else 0 for j in range(UpperCamelCase__      )] for i in range(UpperCamelCase__      )]
  	# stores tree roots that will be used later for constructing binary search tree
  	_UpperCAmelCase =						[[i if i == j else 0 for j in range(UpperCamelCase__      )] for i in range(UpperCamelCase__      )]
  
  	for interval_length in range(2				,     n + 1      ):
  		for i in range(n - interval_length + 1      ):
  			_UpperCAmelCase =						i + interval_length - 1
  
  			_UpperCAmelCase =						sys.maxsize  # set the value to "infinity"
  			_UpperCAmelCase =						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 =						dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
  				_UpperCAmelCase =						dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
  				_UpperCAmelCase =						left + total[i][j] + right
  
  				if dp[i][j] > cost:
  					_UpperCAmelCase =						cost
  					_UpperCAmelCase =						r
  
  	print("Binary search tree nodes:"      )
  	for node in nodes:
  		print(UpperCamelCase__      )
  
  	print(f"\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}."      )
  	print_binary_search_tree(UpperCamelCase__				,     UpperCamelCase__				,     0				,     n - 1				,     -1				,     UpperCamelCase__      )
  
  
  
  
  def     __lowerCamelCase  (		):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						[Node(UpperCamelCase__				,     randint(1				,     50      )      ) for i in range(10				,     0				,     -1      )]
  	find_optimal_binary_search_tree(UpperCamelCase__      )
  
  
  if __name__ == "__main__":
  			main()
  
  
  
  
  
style_context: 
  """simple docstring"""
  import subprocess
  from typing import Union
  
  import numpy as np
  import requests
  
  from ..utils import add_end_docstrings, is_torch_available, is_torchaudio_available, logging
  from .base import PIPELINE_INIT_ARGS, Pipeline
  
  
  if is_torch_available():
  			from ..models.auto.modeling_auto import MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING
  
  __magic_name__		       =				logging.get_logger(__name__)
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						f"{sampling_rate}"
  	_UpperCAmelCase =						"1"
  	_UpperCAmelCase =						"f32le"
  	_UpperCAmelCase =						[
  	    "ffmpeg",
  	    "-i",
  	    "pipe:0",
  	    "-ac",
  	    ac,
  	    "-ar",
  	    ar,
  	    "-f",
  	    format_for_conversion,
  	    "-hide_banner",
  	    "-loglevel",
  	    "quiet",
  	    "pipe:1",
  	]
  
  	try:
  		_UpperCAmelCase =						subprocess.Popen(UpperCamelCase__				,     stdin=subprocess.PIPE				,     stdout=subprocess.PIPE      )
  	except FileNotFoundError:
  		raise ValueError("ffmpeg was not found but is required to load audio files from filename"      )
  	_UpperCAmelCase =						ffmpeg_process.communicate(UpperCamelCase__      )
  	_UpperCAmelCase =						output_stream[0]
  
  	_UpperCAmelCase =						np.frombuffer(UpperCamelCase__				,     np.floataa      )
  	if audio.shape[0] == 0:
  		raise ValueError("Malformed soundfile"      )
  	return audio
  
  
  
  @add_end_docstrings(lowerCamelCase						)
  class    _lowerCAmelCase						(						lowerCamelCase						):
  
  
  
  							def __init__(      self ,						*a_ ,						**a_   )							->							Union[str, Any]:
  								# Default, might be overriden by the model.config.
  								_UpperCAmelCase =						5
  								super().__init__(*a_ ,						**a_   )
  
  								if self.framework != "pt":
  									raise ValueError(f"The {self.__class__} is only available in PyTorch."   )
  
  								self.check_model_type(a_   )
  
  
  
  							def __call__(      self ,						a_ ,						**a_ ,						)							->							int:
  								return super().__call__(a_ ,						**a_   )
  
  
  
  							def       _a   (      self ,						a_=None ,						**a_   )							->							Dict:
  								# No parameters on this pipeline right now
  								_UpperCAmelCase =						{}
  								if top_k is not None:
  									if top_k > self.model.config.num_labels:
  										_UpperCAmelCase =						self.model.config.num_labels
  									_UpperCAmelCase =						top_k
  								return {}, {}, postprocess_params
  
  
  
  							def       _a   (      self ,						a_   )							->							str:
  								if isinstance(a_ ,						a_   ):
  									if inputs.startswith("http://"   ) or inputs.startswith("https://"   ):
  										# We need to actually check for a real protocol, otherwise it's impossible to use a local file
  										# like http_huggingface_co.png
  										_UpperCAmelCase =						requests.get(a_   ).content
  									else:
  										with open(a_ ,						"rb"   ) as f:
  											_UpperCAmelCase =						f.read()
  
  								if isinstance(a_ ,						a_   ):
  									_UpperCAmelCase =						ffmpeg_read(a_ ,						self.feature_extractor.sampling_rate   )
  
  								if isinstance(a_ ,						a_   ):
  									# Accepting `"array"` which is the key defined in `datasets` for
  									# better integration
  									if not ("sampling_rate" in inputs and ("raw" in inputs or "array" in inputs)):
  										raise ValueError(
  										    "When passing a dictionary to AudioClassificationPipeline, the dict needs to contain a "
  										    "\"raw\" key containing the numpy array representing the audio and a \"sampling_rate\" key, "
  										    "containing the sampling_rate associated with that array"   )
  
  									_UpperCAmelCase =						inputs.pop("raw" ,						a_   )
  									if _inputs is None:
  										# Remove path which will not be used from `datasets`.
  										inputs.pop("path" ,						a_   )
  										_UpperCAmelCase =						inputs.pop("array" ,						a_   )
  									_UpperCAmelCase =						inputs.pop("sampling_rate"   )
  									_UpperCAmelCase =						_inputs
  									if in_sampling_rate != self.feature_extractor.sampling_rate:
  										import torch
  
  										if is_torchaudio_available():
  											from torchaudio import functional as F
  										else:
  											raise ImportError(
  											    "torchaudio is required to resample audio samples in AudioClassificationPipeline. "
  											    "The torchaudio package can be installed through: `pip install torchaudio`."   )
  
  										_UpperCAmelCase =						F.resample(
  										    torch.from_numpy(a_   ) ,						a_ ,						self.feature_extractor.sampling_rate   ).numpy()
  
  								if not isinstance(a_ ,						np.ndarray   ):
  									raise ValueError("We expect a numpy ndarray as input"   )
  								if len(inputs.shape   ) != 1:
  									raise ValueError("We expect a single channel audio input for AudioClassificationPipeline"   )
  
  								_UpperCAmelCase =						self.feature_extractor(
  								    a_ ,						sampling_rate=self.feature_extractor.sampling_rate ,						return_tensors="pt"   )
  								return processed
  
  
  
  							def       _a   (      self ,						a_   )							->							List[str]:
  								_UpperCAmelCase =						self.model(**a_   )
  								return model_outputs
  
  
  
  							def       _a   (      self ,						a_ ,						a_=5   )							->							int:
  								_UpperCAmelCase =						model_outputs.logits[0].softmax(-1   )
  								_UpperCAmelCase ,      _UpperCAmelCase =						probs.topk(a_   )
  
  								_UpperCAmelCase =						scores.tolist()
  								_UpperCAmelCase =						ids.tolist()
  
  								_UpperCAmelCase =						[{"score": score, "label": self.model.config.idalabel[_id]} for score, _id in zip(a_ ,						a_   )]
  
  								return labels
  
  
  
  
  