

'''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        lowercase_	:

  '''simple docstring'''





  def __init__(     self   , a_   , a_     )							->				str:


    """simple docstring"""
    UpperCAmelCase													=	key
    UpperCAmelCase													=	freq





  def __str__(     self     )							->				Optional[int]:


    """simple docstring"""
    return F'''Node(key={self.key}, freq={self.freq})'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   List[str]       ,   SCREAMING_SNAKE_CASE      :   List[Any]       ,   SCREAMING_SNAKE_CASE      :   Optional[int]       ,   SCREAMING_SNAKE_CASE      :   str       ,   SCREAMING_SNAKE_CASE      :   Optional[int]       ,   SCREAMING_SNAKE_CASE      :   Any						):
  if i > j or i < 0 or j > len(SCREAMING_SNAKE_CASE						) - 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(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       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   str						):
  nodes.sort(key=lambda SCREAMING_SNAKE_CASE						: node.key						)

  UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	[nodes[i].key for i in range(SCREAMING_SNAKE_CASE						)]
  UpperCAmelCase													=	[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.
  UpperCAmelCase													=	[[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
  UpperCAmelCase													=	[[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
  UpperCAmelCase													=	[[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						):
      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(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       lowerCamelCase__		(						):
  # A sample binary search tree
  UpperCAmelCase													=	[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, prepare_image_inputs


if is_torch_available():
  import torch

if is_vision_available():
  from PIL import Image

  from transformers import MobileNetVaImageProcessor



class        lowercase_	(		unittest.TestCase ):

  '''simple docstring'''





  def __init__(     self   , a_   , a_=7   , a_=3   , a_=1_8   , a_=3_0   , a_=4_0_0   , a_=True   , a_=None   , a_=True   , a_=None   , )							->				List[str]:


    """simple docstring"""
    UpperCAmelCase													=	size if size is not None else {'shortest_edge': 2_0}
    UpperCAmelCase													=	crop_size if crop_size is not None else {'height': 1_8, 'width': 1_8}
    UpperCAmelCase													=	parent
    UpperCAmelCase													=	batch_size
    UpperCAmelCase													=	num_channels
    UpperCAmelCase													=	image_size
    UpperCAmelCase													=	min_resolution
    UpperCAmelCase													=	max_resolution
    UpperCAmelCase													=	do_resize
    UpperCAmelCase													=	size
    UpperCAmelCase													=	do_center_crop
    UpperCAmelCase													=	crop_size





  def 						snake_case_			(     self     )							->				Optional[int]:


    """simple docstring"""
    return {
        "do_resize": self.do_resize,
        "size": self.size,
        "do_center_crop": self.do_center_crop,
        "crop_size": self.crop_size,
    }




@require_torch
@require_vision
class        lowercase_	(		a ,       unittest.TestCase ):

  '''simple docstring'''





  __lowerCAmelCase					: Union[str, Any]      =   MobileNetVaImageProcessor if is_vision_available() else None
  def 						snake_case_			(     self     )							->				Dict:


    """simple docstring"""
    UpperCAmelCase													=	MobileNetVaImageProcessingTester(self     )
  @property
  def 						snake_case_			(     self     )							->				List[str]:


    """simple docstring"""
    return self.image_processor_tester.prepare_image_processor_dict()
  def 						snake_case_			(     self     )							->				Optional[int]:


    """simple docstring"""
    UpperCAmelCase													=	self.image_processing_class(**self.image_processor_dict     )
    self.assertTrue(hasattr(a_   , 'do_resize'     )     )
    self.assertTrue(hasattr(a_   , 'size'     )     )
    self.assertTrue(hasattr(a_   , 'do_center_crop'     )     )
    self.assertTrue(hasattr(a_   , 'center_crop'     )     )
  def 						snake_case_			(     self     )							->				str:


    """simple docstring"""
    UpperCAmelCase													=	self.image_processing_class.from_dict(self.image_processor_dict     )
    self.assertEqual(image_processor.size   , {'shortest_edge': 2_0}     )
    self.assertEqual(image_processor.crop_size   , {'height': 1_8, 'width': 1_8}     )

    UpperCAmelCase													=	self.image_processing_class.from_dict(self.image_processor_dict   , size=4_2   , crop_size=8_4     )
    self.assertEqual(image_processor.size   , {'shortest_edge': 4_2}     )
    self.assertEqual(image_processor.crop_size   , {'height': 8_4, 'width': 8_4}     )
  def 						snake_case_			(     self     )							->				List[str]:


    """simple docstring"""
    pass
  def 						snake_case_			(     self     )							->				List[Any]:


    """simple docstring"""
    # Initialize image_processing
    UpperCAmelCase													=	self.image_processing_class(**self.image_processor_dict     )
    # create random PIL images
    UpperCAmelCase													=	prepare_image_inputs(self.image_processor_tester   , equal_resolution=a_     )
    for image in image_inputs:
      self.assertIsInstance(a_   , Image.Image     )

    # Test not batched input
    UpperCAmelCase													=	image_processing(image_inputs[0]   , return_tensors='pt'     ).pixel_values
    self.assertEqual(
        encoded_images.shape   , (
            1,
            self.image_processor_tester.num_channels,
            self.image_processor_tester.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )

    # Test batched
    UpperCAmelCase													=	image_processing(a_   , 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.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )
  def 						snake_case_			(     self     )							->				str:


    """simple docstring"""
    # Initialize image_processing
    UpperCAmelCase													=	self.image_processing_class(**self.image_processor_dict     )
    # create random numpy tensors
    UpperCAmelCase													=	prepare_image_inputs(self.image_processor_tester   , equal_resolution=a_   , numpify=a_     )
    for image in image_inputs:
      self.assertIsInstance(a_   , np.ndarray     )

    # Test not batched input
    UpperCAmelCase													=	image_processing(image_inputs[0]   , return_tensors='pt'     ).pixel_values
    self.assertEqual(
        encoded_images.shape   , (
            1,
            self.image_processor_tester.num_channels,
            self.image_processor_tester.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )

    # Test batched
    UpperCAmelCase													=	image_processing(a_   , 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.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )





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


    """simple docstring"""
    # Initialize image_processing
    UpperCAmelCase													=	self.image_processing_class(**self.image_processor_dict     )
    # create random PyTorch tensors
    UpperCAmelCase													=	prepare_image_inputs(self.image_processor_tester   , equal_resolution=a_   , torchify=a_     )
    for image in image_inputs:
      self.assertIsInstance(a_   , torch.Tensor     )

    # Test not batched input
    UpperCAmelCase													=	image_processing(image_inputs[0]   , return_tensors='pt'     ).pixel_values
    self.assertEqual(
        encoded_images.shape   , (
            1,
            self.image_processor_tester.num_channels,
            self.image_processor_tester.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )

    # Test batched
    UpperCAmelCase													=	image_processing(a_   , 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.crop_size['height'],
            self.image_processor_tester.crop_size['width'],
        )   , )


