




'''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()







'''simple docstring'''





from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxSeqaSeqConfigWithPast
from ...utils import logging


lowercase__								=						logging.get_logger(__name__)






class     lowercase  ( UpperCAmelCase_):
      __lowercase					=	'''mt5'''
      __lowercase					=	['''past_key_values''']






      def __init__(self			,	a__=2_5_0_1_1_2			,	a__=5_1_2			,	a__=6_4			,	a__=1_0_2_4			,	a__=8			,	a__=None			,	a__=6			,	a__=3_2			,	a__=1_2_8			,	a__=0.1			,	a__=1E-6			,	a__=1.0			,	a__="gated-gelu"			,	a__=True			,	a__=True			,	a__="T5Tokenizer"			,	a__=False			,	a__=0			,	a__=1			,	a__=0			,	**a__			,	)							-> List[Any]:
         super().__init__(
             is_encoder_decoder=a__			,	tokenizer_class=a__			,	tie_word_embeddings=a__			,	pad_token_id=a__			,	eos_token_id=a__			,	decoder_start_token_id=a__			,	**a__			,	)
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			vocab_size
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			d_model
         SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			d_kv
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			d_ff
         SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			num_layers
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			(
             num_decoder_layers if num_decoder_layers is not None else self.num_layers
         )  # default = symmetry
         SCREAMING_SNAKE_CASE__      :					Any							    =			num_heads
         SCREAMING_SNAKE_CASE__      :					Any							    =			relative_attention_num_buckets
         SCREAMING_SNAKE_CASE__      :					Any							    =			relative_attention_max_distance
         SCREAMING_SNAKE_CASE__      :					Any							    =			dropout_rate
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			layer_norm_epsilon
         SCREAMING_SNAKE_CASE__      :					List[str]							    =			initializer_factor
         SCREAMING_SNAKE_CASE__      :					List[Any]							    =			feed_forward_proj
         SCREAMING_SNAKE_CASE__      :					Any							    =			use_cache

         SCREAMING_SNAKE_CASE__      :					int							    =			self.feed_forward_proj.split('''-'''       )
         SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			act_info[-1]
         SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			act_info[0] == '''gated'''

         if len(a__       ) > 1 and act_info[0] != "gated" or len(a__       ) > 2:
            raise ValueError(
                f"""`feed_forward_proj`: {feed_forward_proj} is not a valid activation function of the dense layer."""
                '''Please make sure `feed_forward_proj` is of the format `gated-{ACT_FN}` or `{ACT_FN}`, e.g. '''
                '''\'gated-gelu\' or \'relu\''''       )

         # for backwards compatibility
         if feed_forward_proj == "gated-gelu":
            SCREAMING_SNAKE_CASE__      :					int							    =			'''gelu_new'''






      @property
      def  A__(self       )							-> Dict:
         return self.d_model






      @property
      def  A__(self       )							-> Tuple:
         return self.num_heads






      @property
      def  A__(self       )							-> List[str]:
         return self.num_layers






class     lowercase  ( UpperCAmelCase_):






      @property
      # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
      def  A__(self       )							-> Mapping[str, Mapping[int, str]]:
         SCREAMING_SNAKE_CASE__      :					List[Any]							    =			{
             '''input_ids''': {0: '''batch''', 1: '''encoder_sequence'''},
             '''attention_mask''': {0: '''batch''', 1: '''encoder_sequence'''},
         }
         if self.use_past:
            SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			'''past_encoder_sequence + sequence'''
            SCREAMING_SNAKE_CASE__      :					str							    =			{0: '''batch'''}
            SCREAMING_SNAKE_CASE__      :					List[Any]							    =			{0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
         else:
            SCREAMING_SNAKE_CASE__      :					int							    =			{0: '''batch''', 1: '''decoder_sequence'''}
            SCREAMING_SNAKE_CASE__      :					Tuple							    =			{0: '''batch''', 1: '''decoder_sequence'''}

         if self.use_past:
            self.fill_with_past_key_values_(a__			,	direction='''inputs'''       )

         return common_inputs






      @property
      # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
      def  A__(self       )							-> int:
         return 1_3






      @property
      def  A__(self       )							-> float:
         return 5E-4

