




# 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 		__UpperCAmelCase:





     """simple docstring"""



     def __init__(      self :       Optional[int]						,				A :       Optional[Any]						,				A :       Any    )			->			List[str]:






         """simple docstring"""
         a__      =       key
         a__      =       freq






     def __str__(      self :       Dict    )			->			str:






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






def        __lowerCAmelCase (UpperCAmelCase_   ,    UpperCAmelCase_   ,    UpperCAmelCase_   ,    UpperCAmelCase_   ,    UpperCAmelCase_   ,    UpperCAmelCase_		):
    if i > j or i < 0 or j > len(UpperCAmelCase_		) - 1:
        return

    a__      =       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_		):
    nodes.sort(key=lambda UpperCAmelCase_		: node.key		)

    a__      =       len(UpperCAmelCase_		)

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

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

                if dp[i][j] > cost:
                    a__      =       cost
                    a__      =       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 ():
    # A sample binary search tree
    a__      =       [Node(UpperCAmelCase_   ,    randint(1   ,    50		)		) for i in range(10   ,    0   ,    -1		)]
    find_optimal_binary_search_tree(UpperCAmelCase_		)


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


if is_torch_available():
 import torch

if is_vision_available():
 from PIL import Image

 from transformers import SwinaSRImageProcessor
 from transformers.image_transforms import get_image_size







class 		__UpperCAmelCase(		unittest.TestCase ):





     """simple docstring"""



     def __init__(      self :       Optional[int]						,				A :       Dict						,				A :       Union[str, Any]=7						,				A :       List[str]=3						,				A :       Optional[int]=18						,				A :       Optional[int]=30						,				A :       Optional[Any]=4_00						,				A :       Optional[Any]=True						,				A :       Tuple=1 / 2_55						,				A :       Tuple=True						,				A :       Optional[int]=8						,				)			->			Any:






         """simple docstring"""
         a__      =       parent
         a__      =       batch_size
         a__      =       num_channels
         a__      =       image_size
         a__      =       min_resolution
         a__      =       max_resolution
         a__      =       do_rescale
         a__      =       rescale_factor
         a__      =       do_pad
         a__      =       pad_size

     def 				__SCREAMING_SNAKE_CASE		(      self :       List[Any]    )			->			Union[str, Any]:






         """simple docstring"""
         return {
             "do_rescale": self.do_rescale,
             "rescale_factor": self.rescale_factor,
             "do_pad": self.do_pad,
             "pad_size": self.pad_size,
         }






     def 				__SCREAMING_SNAKE_CASE		(      self :       int						,				A :       int=False						,				A :       Any=False						,				A :       List[Any]=False    )			->			Optional[Any]:






         """simple docstring"""
         assert not (numpify and torchify), "You cannot specify both numpy and PyTorch tensors at the same time"

         if equal_resolution:
             a__      =       []
             for i in range(self.batch_size    ):
                 image_inputs.append(
                     np.random.randint(
                         2_55						,				size=(self.num_channels, self.max_resolution, self.max_resolution)						,				dtype=np.uinta    )    )
         else:
             a__      =       []
             for i in range(self.batch_size    ):
                 a__ ,		a__      =       np.random.choice(np.arange(self.min_resolution						,				self.max_resolution    )						,				2    )
                 image_inputs.append(np.random.randint(2_55						,				size=(self.num_channels, width, height)						,				dtype=np.uinta    )    )

         if not numpify and not torchify:
             # PIL expects the channel dimension as last dimension
             a__      =       [Image.fromarray(np.moveaxis(A						,				0						,				-1    )    ) for x in image_inputs]

         if torchify:
             a__      =       [torch.from_numpy(A    ) for x in image_inputs]

         return image_inputs







@require_torch
@require_vision
class 		__UpperCAmelCase(		lowercase__       ,	unittest.TestCase ):





     """simple docstring"""



     __UpperCAmelCase	: Dict						=    SwinaSRImageProcessor if is_vision_available() else None

     def 				__SCREAMING_SNAKE_CASE		(      self :       int    )			->			Dict:






         """simple docstring"""
         a__      =       SwinaSRImageProcessingTester(self    )

     @property
     def 				__SCREAMING_SNAKE_CASE		(      self :       List[Any]    )			->			List[Any]:






         """simple docstring"""
         return self.image_processor_tester.prepare_image_processor_dict()

     def 				__SCREAMING_SNAKE_CASE		(      self :       Tuple    )			->			int:






         """simple docstring"""
         a__      =       self.image_processing_class(**self.image_processor_dict    )
         self.assertTrue(hasattr(A						,				"""do_rescale"""    )    )
         self.assertTrue(hasattr(A						,				"""rescale_factor"""    )    )
         self.assertTrue(hasattr(A						,				"""do_pad"""    )    )
         self.assertTrue(hasattr(A						,				"""pad_size"""    )    )

     def 				__SCREAMING_SNAKE_CASE		(      self :       Dict    )			->			List[Any]:






         """simple docstring"""
         pass

     def 				__SCREAMING_SNAKE_CASE		(      self :       int						,				A :       Optional[Any]    )			->			List[str]:






         """simple docstring"""
         a__ ,		a__      =       get_image_size(A    )
         a__      =       self.image_processor_tester.pad_size

         a__      =       (old_height // size + 1) * size - old_height
         a__      =       (old_width // size + 1) * size - old_width
         return old_height + pad_height, old_width + pad_width

     def 				__SCREAMING_SNAKE_CASE		(      self :       Any    )			->			Union[str, Any]:






         """simple docstring"""
         # Initialize image_processor
         a__      =       self.image_processing_class(**self.image_processor_dict    )
         # create random PIL images
         a__      =       self.image_processor_tester.prepare_inputs(equal_resolution=A    )
         for image in image_inputs:
             self.assertIsInstance(A						,				Image.Image    )

         # Test not batched input
         a__      =       image_processor(image_inputs[0]						,				return_tensors="""pt"""    ).pixel_values
         a__ ,		a__      =       self.calculate_expected_size(np.array(image_inputs[0]    )    )
         self.assertEqual(
             encoded_images.shape						,				(
                 1,
                 self.image_processor_tester.num_channels,
                 expected_height,
                 expected_width,
             )						,				)

     def 				__SCREAMING_SNAKE_CASE		(      self :       Union[str, Any]    )			->			Optional[Any]:






         """simple docstring"""
         # Initialize image_processor
         a__      =       self.image_processing_class(**self.image_processor_dict    )
         # create random numpy tensors
         a__      =       self.image_processor_tester.prepare_inputs(equal_resolution=A						,				numpify=A    )
         for image in image_inputs:
             self.assertIsInstance(A						,				np.ndarray    )

         # Test not batched input
         a__      =       image_processor(image_inputs[0]						,				return_tensors="""pt"""    ).pixel_values
         a__ ,		a__      =       self.calculate_expected_size(image_inputs[0]    )
         self.assertEqual(
             encoded_images.shape						,				(
                 1,
                 self.image_processor_tester.num_channels,
                 expected_height,
                 expected_width,
             )						,				)






     def 				__SCREAMING_SNAKE_CASE		(      self :       Union[str, Any]    )			->			Tuple:






         """simple docstring"""
         # Initialize image_processor
         a__      =       self.image_processing_class(**self.image_processor_dict    )
         # create random PyTorch tensors
         a__      =       self.image_processor_tester.prepare_inputs(equal_resolution=A						,				torchify=A    )
         for image in image_inputs:
             self.assertIsInstance(A						,				torch.Tensor    )

         # Test not batched input
         a__      =       image_processor(image_inputs[0]						,				return_tensors="""pt"""    ).pixel_values
         a__ ,		a__      =       self.calculate_expected_size(image_inputs[0]    )
         self.assertEqual(
             encoded_images.shape						,				(
                 1,
                 self.image_processor_tester.num_channels,
                 expected_height,
                 expected_width,
             )						,				)






