

"""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      __UpperCamelCase					:


		def __init__(self					:						Dict	,	__SCREAMING_SNAKE_CASE					:						Optional[Any]	,	__SCREAMING_SNAKE_CASE					:						List[str]):
							A     =   key
							A     =   freq


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

def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					if i > j or i < 0 or j > len(lowercase__ ) - 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(lowercase__     ,				lowercase__     ,				lowercase__     ,				node - 1     ,				key[node]     ,				lowercase__ )
					print_binary_search_tree(lowercase__     ,				lowercase__     ,				node + 1     ,				lowercase__     ,				key[node]     ,				lowercase__ )
def   __SCREAMING_SNAKE_CASE		(		lowercase__ ):
					"""simple docstring"""
					nodes.sort(key=lambda lowercase__ : node.key )

					A     =   len(lowercase__ )

					A     =   [nodes[i].key for i in range(lowercase__ )]
					A     =   [nodes[i].freq for i in range(lowercase__ )]

					# 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(lowercase__ )] for i in range(lowercase__ )]
					# 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(lowercase__ )] for i in range(lowercase__ )]
					# stores tree roots that will be used later for constructing binary search tree
					A     =   [[i if i == j else 0 for j in range(lowercase__ )] for i in range(lowercase__ )]

					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(lowercase__ )

					print(F"""\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.""" )
					print_binary_search_tree(lowercase__     ,				lowercase__     ,				0     ,				n - 1     ,				-1     ,				lowercase__ )
def   __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					# A sample binary search tree
					A     =   [Node(lowercase__     ,				randint(1     ,				50 ) ) for i in range(10     ,				0     ,				-1 )]
					find_optimal_binary_search_tree(lowercase__ )


if __name__ == "__main__":
	main()









'''simple docstring'''






import copy
from typing import Dict, Optional

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto import CONFIG_MAPPING


a_       :     List[str] 							=     logging.get_logger(__name__)

a_       :     Union[str, Any] 							=     {
    "shi-labs/oneformer_ade20k_swin_tiny": (
        "https://huggingface.co/shi-labs/oneformer_ade20k_swin_tiny/blob/main/config.json"
    ),
    # See all OneFormer models at https://huggingface.co/models?filter=oneformer
}




class 			a  (  _SCREAMING_SNAKE_CASE							):
 _lowerCAmelCase			       =						"""oneformer"""
 _lowerCAmelCase			       =						{"""hidden_size""": """hidden_dim"""}
 def __init__(			self   ,					__magic_name__ = None   ,					__magic_name__ = 2_55   ,					__magic_name__ = 1_50   ,					__magic_name__ = 0.1   ,					__magic_name__ = 2.0   ,					__magic_name__ = 5.0   ,					__magic_name__ = 5.0   ,					__magic_name__ = 0.5   ,					__magic_name__ = 0.0_7   ,					__magic_name__ = 1_25_44   ,					__magic_name__ = 3.0   ,					__magic_name__ = 0.7_5   ,					__magic_name__ = 0.0_2   ,					__magic_name__ = 1.0   ,					__magic_name__ = 1e-05   ,					__magic_name__ = False   ,					__magic_name__ = True   ,					__magic_name__ = True   ,					__magic_name__ = [4, 8, 16, 32]   ,					__magic_name__ = 77   ,					__magic_name__ = 2_56   ,					__magic_name__ = 77   ,					__magic_name__ = 6   ,					__magic_name__ = 4_94_08   ,					__magic_name__ = 2   ,					__magic_name__ = 16   ,					__magic_name__ = 2_56   ,					__magic_name__ = 2_56   ,					__magic_name__ = 2_56   ,					__magic_name__ = 10_24   ,					__magic_name__ = "GN"   ,					__magic_name__ = 6   ,					__magic_name__ = 10   ,					__magic_name__ = True   ,					__magic_name__ = 8   ,					__magic_name__ = 0.1   ,					__magic_name__ = 20_48   ,					__magic_name__ = False   ,					__magic_name__ = False   ,					__magic_name__ = 2   ,					__magic_name__ = 4   ,					**__magic_name__   ,					)       ->				Dict:
      if backbone_config is None:
           logger.info('`backbone_config` is unset. Initializing the config with the default `Swin` backbone.'    )
           _a         =				CONFIG_MAPPING['swin'](
               image_size=2_24   ,					in_channels=3   ,					patch_size=4   ,					embed_dim=96   ,					depths=[2, 2, 6, 2]   ,					num_heads=[3, 6, 12, 24]   ,					window_size=7   ,					drop_path_rate=0.3   ,					use_absolute_embeddings=__magic_name__   ,					out_features=['stage1', 'stage2', 'stage3', 'stage4']   ,					)
      elif isinstance(__magic_name__   ,					__magic_name__    ):
           _a         =				backbone_config.get('model_type'    )
           _a         =				CONFIG_MAPPING[backbone_model_type]
           _a         =				config_class.from_dict(__magic_name__    )

      _a         =				backbone_config

      _a         =				ignore_value
      _a         =				num_queries
      _a         =				no_object_weight
      _a         =				class_weight
      _a         =				mask_weight
      _a         =				dice_weight
      _a         =				contrastive_weight
      _a         =				contrastive_temperature
      _a         =				train_num_points
      _a         =				oversample_ratio
      _a         =				importance_sample_ratio
      _a         =				init_std
      _a         =				init_xavier_std
      _a         =				layer_norm_eps
      _a         =				is_training
      _a         =				use_auxiliary_loss
      _a         =				output_auxiliary_logits
      _a         =				strides
      _a         =				task_seq_len
      _a         =				text_encoder_width
      _a         =				text_encoder_context_length
      _a         =				text_encoder_num_layers
      _a         =				text_encoder_vocab_size
      _a         =				text_encoder_proj_layers
      _a         =				text_encoder_n_ctx
      _a         =				conv_dim
      _a         =				mask_dim
      _a         =				hidden_dim
      _a         =				encoder_feedforward_dim
      _a         =				norm
      _a         =				encoder_layers
      _a         =				decoder_layers
      _a         =				use_task_norm
      _a         =				num_attention_heads
      _a         =				dropout
      _a         =				dim_feedforward
      _a         =				pre_norm
      _a         =				enforce_input_proj
      _a         =				query_dec_layers
      _a         =				common_stride
      _a         =				decoder_layers

      super().__init__(**__magic_name__    )




 def 				__UpperCAmelCase		(			self    )       ->				Dict[str, any]:
      _a         =				copy.deepcopy(self.__dict__    )
      _a         =				self.backbone_config.to_dict()
      _a         =				self.__class__.model_type
      return output

