



"""simple docstring"""


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__)











'''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     lowercase  :






      def __init__(self			,	a__			,	a__       )							-> Optional[int]:
         SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			key
         SCREAMING_SNAKE_CASE__      :					List[Any]							    =			freq






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


def 					UpperCamelCase						(	snake_case						,  snake_case						,  snake_case						,  snake_case						,  snake_case						,  snake_case ):




   '''simple docstring'''

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

   SCREAMING_SNAKE_CASE__      :					Tuple							    =			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 					UpperCamelCase						(	snake_case ):




   '''simple docstring'''

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

   SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			len(snake_case )

   SCREAMING_SNAKE_CASE__      :					List[str]							    =			[nodes[i].key for i in range(snake_case )]
   SCREAMING_SNAKE_CASE__      :					int							    =			[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.
   SCREAMING_SNAKE_CASE__      :					Dict							    =			[[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
   SCREAMING_SNAKE_CASE__      :					str							    =			[[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
   SCREAMING_SNAKE_CASE__      :					int							    =			[[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 ):
         SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			i + interval_length - 1

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

            if dp[i][j] > cost:
               SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			cost
               SCREAMING_SNAKE_CASE__      :					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 					UpperCamelCase						(	):




   '''simple docstring'''

   SCREAMING_SNAKE_CASE__      :					Optional[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()

