

# 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  ,  _UpperCAmelCase  ,  _UpperCAmelCase							):
   __UpperCAmelCase	:  Union[str, Any]		=     key
   __UpperCAmelCase	:  Tuple		=     freq




 def __str__(			self							):
   return F"Node(key={self.key}, freq={self.freq})"





def  _snake_case		(snake_case_					:     Union[str, Any]    ,       snake_case_					:     Optional[int]    ,       snake_case_					:     Any    ,       snake_case_					:     Any    ,       snake_case_					:     Tuple    ,       snake_case_					:     Tuple  )							->		Tuple:
  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  _snake_case		(snake_case_					:     Union[str, Any]  )							->		Any:
  nodes.sort(key=lambda snake_case_  : node.key  )

  __UpperCAmelCase	:  Optional[Any]		=     len(snake_case_  )

  __UpperCAmelCase	:  int		=     [nodes[i].key for i in range(snake_case_  )]
  __UpperCAmelCase	:  Dict		=     [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	:  int		=     [[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	:  Any		=     [[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	:  Tuple		=     [[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	:  int		=     sys.maxsize  # set the value to "infinity"
      __UpperCAmelCase	:  List[str]		=     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	:  Union[str, Any]		=     dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
        __UpperCAmelCase	:  List[Any]		=     dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
        __UpperCAmelCase	:  List[Any]		=     left + total[i][j] + right

        if dp[i][j] > cost:
          __UpperCAmelCase	:  Tuple		=     cost
          __UpperCAmelCase	:  str		=     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  _snake_case		()							->		Any:
  # A sample binary search tree
  __UpperCAmelCase	:  List[Any]		=     [Node(snake_case_    ,       randint(1    ,       50  )  ) for i in range(10    ,       0    ,       -1  )]
  find_optimal_binary_search_tree(snake_case_  )


if __name__ == "__main__":
      main()











'''simple docstring'''







import inspect
import unittest

from transformers import is_torch_available, is_vision_available
from transformers.models.auto import get_values
from transformers.testing_utils import require_torch, slow, torch_device

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
   import torch

   from transformers import MODEL_MAPPING, PoolFormerConfig, PoolFormerForImageClassification, PoolFormerModel
   from transformers.models.poolformer.modeling_poolformer import POOLFORMER_PRETRAINED_MODEL_ARCHIVE_LIST


if is_vision_available():
   from PIL import Image

   from transformers import PoolFormerImageProcessor


class      _a    (      __a					):
       def        A (      self		:      Tuple							):



           '''simple docstring'''

           UpperCAmelCase     			=						self.config_class(**self.inputs_dict							)
           self.parent.assertTrue(hasattr(lowercase  ,							'''hidden_sizes'''							)							)
           self.parent.assertTrue(hasattr(lowercase  ,							'''num_encoder_blocks'''							)							)






class      _a    :
       def __init__(      self		:      Any  ,							lowercase		:      Any  ,							lowercase		:      Optional[Any]=13  ,							lowercase		:      List[str]=64  ,							lowercase		:      Optional[Any]=3  ,							lowercase		:      List[str]=4  ,							lowercase		:      Optional[int]=[2, 2, 2, 2]  ,							lowercase		:      Tuple=[8, 4, 2, 1]  ,							lowercase		:      Optional[int]=[16, 32, 64, 128]  ,							lowercase		:      Tuple=[1, 4, 8, 16]  ,							lowercase		:      List[Any]=False  ,							lowercase		:      List[Any]=True  ,							lowercase		:      List[str]="gelu"  ,							lowercase		:      Any=0.1  ,							lowercase		:      Dict=0.02  ,							lowercase		:      str=3  ,							lowercase		:      Optional[Any]=None  ,							):



           '''simple docstring'''

           UpperCAmelCase     			=						parent
           UpperCAmelCase     			=						batch_size
           UpperCAmelCase     			=						image_size
           UpperCAmelCase     			=						num_channels
           UpperCAmelCase     			=						num_encoder_blocks
           UpperCAmelCase     			=						sr_ratios
           UpperCAmelCase     			=						depths
           UpperCAmelCase     			=						hidden_sizes
           UpperCAmelCase     			=						downsampling_rates
           UpperCAmelCase     			=						is_training
           UpperCAmelCase     			=						use_labels
           UpperCAmelCase     			=						hidden_act
           UpperCAmelCase     			=						hidden_dropout_prob
           UpperCAmelCase     			=						initializer_range
           UpperCAmelCase     			=						num_labels
           UpperCAmelCase     			=						scope
       def        A (      self		:      Union[str, Any]							):



           '''simple docstring'''

           UpperCAmelCase     			=						floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]							)

           UpperCAmelCase     			=						None
           if self.use_labels:
               UpperCAmelCase     			=						ids_tensor([self.batch_size, self.image_size, self.image_size]  ,							self.num_labels							)

           UpperCAmelCase     			=						PoolFormerConfig(
               image_size=self.image_size  ,							num_channels=self.num_channels  ,							num_encoder_blocks=self.num_encoder_blocks  ,							depths=self.depths  ,							hidden_sizes=self.hidden_sizes  ,							hidden_act=self.hidden_act  ,							hidden_dropout_prob=self.hidden_dropout_prob  ,							initializer_range=self.initializer_range  ,							)

           return config, pixel_values, labels
       def        A (      self		:      Optional[Any]  ,							lowercase		:      List[Any]  ,							lowercase		:      Dict  ,							lowercase		:      Union[str, Any]							):



           '''simple docstring'''

           UpperCAmelCase     			=						PoolFormerModel(config=lowercase							)
           model.to(lowercase							)
           model.eval()
           UpperCAmelCase     			=						model(lowercase							)
           UpperCAmelCase     			=						UpperCAmelCase     			=						self.image_size // 32.0
           self.parent.assertEqual(
               result.last_hidden_state.shape  ,							(self.batch_size, self.hidden_sizes[-1], expected_height, expected_width)							)







       def        A (      self		:      Union[str, Any]							):



           '''simple docstring'''

           UpperCAmelCase     			=						self.prepare_config_and_inputs()
           UpperCAmelCase			,	UpperCAmelCase			,	UpperCAmelCase     			=						config_and_inputs
           UpperCAmelCase     			=						{'''pixel_values''': pixel_values}
           return config, inputs_dict






@require_torch
class      _a    (      __a				,				__a				,				unittest.TestCase					):
       __a							:	Optional[int]  							=   (PoolFormerModel, PoolFormerForImageClassification) if is_torch_available() else ()
       __a							:	Dict  							=   (
           {"""feature-extraction""": PoolFormerModel, """image-classification""": PoolFormerForImageClassification}
           if is_torch_available()
           else {}
       )

       __a							:	str  							=   False
       __a							:	Optional[int]  							=   False
       __a							:	Tuple  							=   False
       __a							:	Union[str, Any]  							=   False
       __a							:	Dict  							=   False
       def        A (      self		:      Any							):



           '''simple docstring'''

           UpperCAmelCase     			=						PoolFormerModelTester(self							)
           UpperCAmelCase     			=						PoolFormerConfigTester(self  ,							config_class=lowercase							)
       def        A (      self		:      Any							):



           '''simple docstring'''

           self.config_tester.run_common_tests()
       def        A (      self		:      Optional[int]							):



           '''simple docstring'''

           UpperCAmelCase     			=						self.model_tester.prepare_config_and_inputs()
           self.model_tester.create_and_check_model(*lowercase							)
       @unittest.skip('''PoolFormer does not use inputs_embeds'''							)
       def        A (      self		:      Dict							):



           '''simple docstring'''

           pass
       @unittest.skip('''PoolFormer does not have get_input_embeddings method and get_output_embeddings methods'''							)
       def        A (      self		:      Union[str, Any]							):



           '''simple docstring'''

           pass
       def        A (      self		:      Dict							):



           '''simple docstring'''

           def check_hidden_states_output(lowercase		:      int  ,							lowercase		:      Any  ,							lowercase		:      Union[str, Any]							):
               UpperCAmelCase     			=						model_class(lowercase							)
               model.to(lowercase							)
               model.eval()

               with torch.no_grad():
                   UpperCAmelCase     			=						model(**self._prepare_for_class(lowercase  ,							lowercase							)							)

               UpperCAmelCase     			=						outputs.hidden_states

               UpperCAmelCase     			=						self.model_tester.num_encoder_blocks
               self.assertEqual(len(lowercase							)  ,							lowercase							)

               # verify the first hidden states (first block)
               self.assertListEqual(
                   list(hidden_states[0].shape[-3:]							)  ,							[
                       self.model_tester.hidden_sizes[0],
                       self.model_tester.image_size // 4,
                       self.model_tester.image_size // 4,
                   ]  ,							)

           UpperCAmelCase			,	UpperCAmelCase     			=						self.model_tester.prepare_config_and_inputs_for_common()

           for model_class in self.all_model_classes:
               UpperCAmelCase     			=						True
               check_hidden_states_output(lowercase  ,							lowercase  ,							lowercase							)

               # check that output_hidden_states also work using config
               del inputs_dict["output_hidden_states"]
               UpperCAmelCase     			=						True

               check_hidden_states_output(lowercase  ,							lowercase  ,							lowercase							)
       def        A (      self		:      Optional[Any]							):



           '''simple docstring'''

           if not self.model_tester.is_training:
               return

           UpperCAmelCase			,	UpperCAmelCase     			=						self.model_tester.prepare_config_and_inputs_for_common()
           UpperCAmelCase     			=						True

           for model_class in self.all_model_classes:
               if model_class in get_values(lowercase							):
                   continue
               UpperCAmelCase     			=						model_class(lowercase							)
               model.to(lowercase							)
               model.train()
               UpperCAmelCase     			=						self._prepare_for_class(lowercase  ,							lowercase  ,							return_labels=lowercase							)
               UpperCAmelCase     			=						model(**lowercase							).loss
               loss.backward()
       def        A (      self		:      str							):



           '''simple docstring'''

           UpperCAmelCase			,	UpperCAmelCase     			=						self.model_tester.prepare_config_and_inputs_for_common()

           for model_class in self.all_model_classes:
               UpperCAmelCase     			=						model_class(lowercase							)
               UpperCAmelCase     			=						inspect.signature(model.forward							)
               # signature.parameters is an OrderedDict => so arg_names order is deterministic
               UpperCAmelCase     			=						[*signature.parameters.keys()]

               UpperCAmelCase     			=						['''pixel_values''']
               self.assertListEqual(arg_names[:1]  ,							lowercase							)







       @slow
       def        A (      self		:      Union[str, Any]							):



           '''simple docstring'''

           for model_name in POOLFORMER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
               UpperCAmelCase     			=						PoolFormerModel.from_pretrained(lowercase							)
               self.assertIsNotNone(lowercase							)






def 		snake_case_				():
    UpperCAmelCase     			=						Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''	)
    return image







@require_torch
class      _a    (      unittest.TestCase					):
       @slow
       def        A (      self		:      str							):



           '''simple docstring'''

           UpperCAmelCase     			=						PoolFormerImageProcessor()
           UpperCAmelCase     			=						PoolFormerForImageClassification.from_pretrained('''sail/poolformer_s12'''							).to(lowercase							)

           UpperCAmelCase     			=						image_processor(images=prepare_img()  ,							return_tensors='''pt'''							).to(lowercase							)

           # forward pass
           with torch.no_grad():
               UpperCAmelCase     			=						model(**lowercase							)

           # verify the logits
           UpperCAmelCase     			=						torch.Size((1, 1_000)							)
           self.assertEqual(outputs.logits.shape  ,							lowercase							)

           UpperCAmelCase     			=						torch.tensor([-0.6113, 0.1685, -0.0492]							).to(lowercase							)
           self.assertTrue(torch.allclose(outputs.logits[0, :3]  ,							lowercase  ,							atol=1E-4							)							)




