

'''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  _snake_case						:






			def __init__(   self       ,_snake_case       ,_snake_case			):
				UpperCAmelCase_			:	Dict      =   key
				UpperCAmelCase_			:	Dict      =   freq






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




def       a__    (  _SCREAMING_SNAKE_CASE					:    Optional[Any]     ,							_SCREAMING_SNAKE_CASE					:    Any     ,							_SCREAMING_SNAKE_CASE					:    int     ,							_SCREAMING_SNAKE_CASE					:    Dict     ,							_SCREAMING_SNAKE_CASE					:    Tuple     ,							_SCREAMING_SNAKE_CASE					:    Optional[int]							)			-> str:


	"""simple docstring"""





	if i > j or i < 0 or j > len(_SCREAMING_SNAKE_CASE							) - 1:
		return

	UpperCAmelCase_			:	Dict      =   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       a__    (  _SCREAMING_SNAKE_CASE					:    Union[str, Any]							)			-> List[Any]:


	"""simple docstring"""





	nodes.sort(key=lambda _SCREAMING_SNAKE_CASE							: node.key							)

	UpperCAmelCase_			:	Optional[Any]      =   len(_SCREAMING_SNAKE_CASE							)

	UpperCAmelCase_			:	str      =   [nodes[i].key for i in range(_SCREAMING_SNAKE_CASE							)]
	UpperCAmelCase_			:	int      =   [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_			:	Any      =   [[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_			:	Optional[int]      =   [[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_			:	Dict      =   [[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_			:	str      =   i + interval_length - 1

			UpperCAmelCase_			:	Optional[Any]      =   sys.maxsize  # set the value to "infinity"
			UpperCAmelCase_			:	int      =   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_			:	str      =   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_			:	List[Any]      =   cost
					UpperCAmelCase_			:	Dict      =   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       a__    (  )			-> Dict:


	"""simple docstring"""





	UpperCAmelCase_			:	Any      =   [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 copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import AutoConfig


_UpperCamelCase				:    Optional[int]     =						logging.get_logger(__name__)






class 						snake_case  (  UpperCAmelCase       ):
    __magic_name__         =     '''speech-encoder-decoder'''
    __magic_name__         =     True





    def __init__(							self	:					Optional[Any]				,		**A	:					List[Any]			):


      '''simple docstring'''




      super().__init__(**A			)
      if "encoder" not in kwargs or "decoder" not in kwargs:
        raise ValueError(
            F'''A configuraton of type {self.model_type} cannot be instantiated because not both `encoder` and'''
            F''' `decoder` sub-configurations are passed, but only {kwargs}'''			)

      a     :			Optional[int]				=   kwargs.pop('encoder'			)
      a     :			Any				=   encoder_config.pop('model_type'			)
      a     :			Optional[Any]				=   kwargs.pop('decoder'			)
      a     :			str				=   decoder_config.pop('model_type'			)

      a     :			Tuple				=   AutoConfig.for_model(A				,		**A			)
      a     :			Dict				=   AutoConfig.for_model(A				,		**A			)
      a     :			Optional[Any]				=   True





    @classmethod
    def 				lowerCamelCase__      (							cls	:					List[Any]				,		A	:					PretrainedConfig				,		A	:					PretrainedConfig				,		**A	:					str			):


      '''simple docstring'''




      logger.info('Setting `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config'			)
      a     :			Any				=   True
      a     :			List[str]				=   True

      return cls(encoder=encoder_config.to_dict()				,		decoder=decoder_config.to_dict()				,		**A			)





    def 				lowerCamelCase__      (							self	:					Optional[int]			):


      '''simple docstring'''




      a     :			List[Any]				=   copy.deepcopy(self.__dict__			)
      a     :			int				=   self.encoder.to_dict()
      a     :			Optional[int]				=   self.decoder.to_dict()
      a     :			Any				=   self.__class__.model_type
      return output




