



"""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     :




	"""simple docstring"""






	def __init__(			self							,UpperCAmelCase_							,UpperCAmelCase_					):
			_lowercase							:      Any			=					key
			_lowercase							:      int			=					freq






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







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

		_lowercase							:      List[Any]			=					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       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		nodes.sort(key=lambda __UpperCAmelCase	: node.key	)

		_lowercase							:      int			=					len(__UpperCAmelCase	)

		_lowercase							:      List[str]			=					[nodes[i].key for i in range(__UpperCAmelCase	)]
		_lowercase							:      List[str]			=					[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.
		_lowercase							:      str			=					[[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
		_lowercase							:      str			=					[[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
		_lowercase							:      List[str]			=					[[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	):
						_lowercase							:      List[Any]			=					i + interval_length - 1

						_lowercase							:      int			=					sys.maxsize  # set the value to "infinity"
						_lowercase							:      Optional[Any]			=					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
								_lowercase							:      List[str]			=					dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
								_lowercase							:      int			=					dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
								_lowercase							:      Tuple			=					left + total[i][j] + right

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


if __name__ == "__main__":
		main()








"""simple docstring"""







from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCAmelCase:   Dict       			=							logging.get_logger(__name__)

UpperCAmelCase:   Optional[Any]       			=							{
    """facebook/opt-125m""": """https://huggingface.co/facebook/opt-125m/blob/main/config.json""",
    """facebook/opt-350m""": """https://huggingface.co/facebook/opt-350m/blob/main/config.json""",
    """facebook/opt-1.3b""": """https://huggingface.co/facebook/opt-1.3b/blob/main/config.json""",
    """facebook/opt-2.7b""": """https://huggingface.co/facebook/opt-2.7b/blob/main/config.json""",
    """facebook/opt-6.7b""": """https://huggingface.co/facebook/opt-6.7b/blob/main/config.json""",
    """facebook/opt-13b""": """https://huggingface.co/facebook/opt-13b/blob/main/config.json""",
}





class    UpperCamelCase     (			snake_case    ):




	"""simple docstring"""
	SCREAMING_SNAKE_CASE_				:    Dict		    =   "opt"
	SCREAMING_SNAKE_CASE_				:    List[str]		    =   ["past_key_values"]






	def __init__(			self							,UpperCAmelCase_=5_02_72							,UpperCAmelCase_=7_68							,UpperCAmelCase_=12							,UpperCAmelCase_=30_72							,UpperCAmelCase_=20_48							,UpperCAmelCase_=True							,UpperCAmelCase_=False							,UpperCAmelCase_=None							,UpperCAmelCase_=0.1							,UpperCAmelCase_=0.0							,UpperCAmelCase_=12							,UpperCAmelCase_="relu"							,UpperCAmelCase_=0.0							,UpperCAmelCase_=0.02							,UpperCAmelCase_=True							,UpperCAmelCase_=1							,UpperCAmelCase_=2							,UpperCAmelCase_=2							,UpperCAmelCase_=True							,UpperCAmelCase_=True							,**UpperCAmelCase_							,):
			super().__init__(
			    pad_token_id=UpperCAmelCase_							,bos_token_id=UpperCAmelCase_							,eos_token_id=UpperCAmelCase_							,**UpperCAmelCase_							,)
			_lowercase							:      Optional[Any]			=					vocab_size
			_lowercase							:      Tuple			=					max_position_embeddings
			_lowercase							:      Union[str, Any]			=					num_attention_heads
			_lowercase							:      List[str]			=					word_embed_proj_dim if word_embed_proj_dim is not None else hidden_size
			_lowercase							:      List[str]			=					ffn_dim
			_lowercase							:      List[str]			=					hidden_size
			_lowercase							:      List[Any]			=					num_hidden_layers
			_lowercase							:      List[Any]			=					dropout
			_lowercase							:      str			=					attention_dropout
			_lowercase							:      List[Any]			=					activation_function
			_lowercase							:      int			=					init_std
			_lowercase							:      List[Any]			=					layerdrop
			_lowercase							:      Tuple			=					use_cache
			_lowercase							:      Any			=					do_layer_norm_before
			# We keep these variables at `True` for backward compatibility.
			_lowercase							:      int			=					enable_bias
			_lowercase							:      str			=					layer_norm_elementwise_affine

			# Note that the only purpose of `_remove_final_layer_norm` is to keep backward compatibility
			# with checkpoints that have been fine-tuned before transformers v4.20.1
			# see https://github.com/facebookresearch/metaseq/pull/164
			_lowercase							:      Optional[Any]			=					_remove_final_layer_norm



