

"""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()









from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


snake_case__  				=			{'configuration_qdqbert': ['QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'QDQBertConfig']}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			snake_case__  				=			[
			    'QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
			    'QDQBertForMaskedLM',
			    'QDQBertForMultipleChoice',
			    'QDQBertForNextSentencePrediction',
			    'QDQBertForQuestionAnswering',
			    'QDQBertForSequenceClassification',
			    'QDQBertForTokenClassification',
			    'QDQBertLayer',
			    'QDQBertLMHeadModel',
			    'QDQBertModel',
			    'QDQBertPreTrainedModel',
			    'load_tf_weights_in_qdqbert',
			]


if TYPE_CHECKING:
			from .configuration_qdqbert import QDQBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, QDQBertConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_qdqbert import (
						    QDQBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    QDQBertForMaskedLM,
						    QDQBertForMultipleChoice,
						    QDQBertForNextSentencePrediction,
						    QDQBertForQuestionAnswering,
						    QDQBertForSequenceClassification,
						    QDQBertForTokenClassification,
						    QDQBertLayer,
						    QDQBertLMHeadModel,
						    QDQBertModel,
						    QDQBertPreTrainedModel,
						    load_tf_weights_in_qdqbert,
						)


else:
			import sys

			snake_case__  				=			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


