'''simple docstring'''


from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
 import torch

snake_case__	:     Union[str, Any]      =    logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
 from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):


 def    _lowerCamelCase       ( cls   :				Dict  ):



      """simple docstring"""





      return cls


def    _lowerCamelCase       ( lowerCamelCase_   :				Union[Tuple, List]      ,	lowerCamelCase_   :				Optional[Union[List["torch.Generator"], "torch.Generator"]] = None      ,	lowerCamelCase_   :				Optional["torch.device"] = None      ,	lowerCamelCase_   :				Optional["torch.dtype"] = None      ,	lowerCamelCase_   :				Optional["torch.layout"] = None      ,	):



     """simple docstring"""





     UpperCAmelCase_				:  Optional[Any]  = device
     UpperCAmelCase_				:  Union[str, Any]  = shape[0]

     UpperCAmelCase_				:  str  = layout or torch.strided
     UpperCAmelCase_				:  Tuple  = device or torch.device('cpu'  )

     if generator is not None:
          UpperCAmelCase_				:  Optional[Any]  = generator.device.type if not isinstance(lowerCamelCase_      ,	lowerCamelCase_  ) else generator[0].device.type
          if gen_device_type != device.type and gen_device_type == "cpu":
               UpperCAmelCase_				:  int  = 'cpu'
               if device != "mps":
                    logger.info(
                        F'''The passed generator was created on \'cpu\' even though a tensor on {device} was expected.'''
                        F''' Tensors will be created on \'cpu\' and then moved to {device}. Note that one can probably'''
                        F''' slighly speed up this function by passing a generator that was created on the {device} device.'''  )
          elif gen_device_type != device.type and gen_device_type == "cuda":
               raise ValueError(F'''Cannot generate a {device} tensor from a generator of type {gen_device_type}.'''  )

     if isinstance(lowerCamelCase_      ,	lowerCamelCase_  ):
          UpperCAmelCase_				:  Optional[Any]  = (1,) + shape[1:]
          UpperCAmelCase_				:  Dict  = [
              torch.randn(lowerCamelCase_      ,	generator=generator[i]      ,	device=lowerCamelCase_      ,	dtype=lowerCamelCase_      ,	layout=lowerCamelCase_  )
              for i in range(lowerCamelCase_  )
          ]
          UpperCAmelCase_				:  Tuple  = torch.cat(lowerCamelCase_      ,	dim=0  ).to(lowerCamelCase_  )
     else:
          UpperCAmelCase_				:  Optional[Any]  = torch.randn(lowerCamelCase_      ,	generator=lowerCamelCase_      ,	device=lowerCamelCase_      ,	dtype=lowerCamelCase_      ,	layout=lowerCamelCase_  ).to(lowerCamelCase_  )

     return latents





def    _lowerCamelCase       ( lowerCamelCase_   :				Any  ):



     """simple docstring"""





     if is_torch_version('<'      ,	'2.0.0'  ) or not hasattr(lowerCamelCase_      ,	'_dynamo'  ):
          return False
     return isinstance(lowerCamelCase_      ,	torch._dynamo.eval_frame.OptimizedModule  )







'''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 	__SCREAMING_SNAKE_CASE		:







  '''simple docstring'''






  def __init__(					self ,						snake_case_ ,						snake_case_		):




       '''simple docstring'''

       UpperCAmelCase_				:  Union[str, Any]  = key
       UpperCAmelCase_				:  Tuple  = freq






  def __str__(					self		):




       '''simple docstring'''

       return F'''Node(key={self.key}, freq={self.freq})'''







def    _lowerCamelCase       ( lowerCamelCase_   :				str      ,	lowerCamelCase_   :				List[str]      ,	lowerCamelCase_   :				Dict      ,	lowerCamelCase_   :				List[Any]      ,	lowerCamelCase_   :				int      ,	lowerCamelCase_   :				Optional[int]  ):



     """simple docstring"""





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

     UpperCAmelCase_				:  Optional[int]  = 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(lowerCamelCase_      ,	lowerCamelCase_      ,	lowerCamelCase_      ,	node - 1      ,	key[node]      ,	lowerCamelCase_  )
     print_binary_search_tree(lowerCamelCase_      ,	lowerCamelCase_      ,	node + 1      ,	lowerCamelCase_      ,	key[node]      ,	lowerCamelCase_  )


def    _lowerCamelCase       ( lowerCamelCase_   :				Optional[int]  ):



     """simple docstring"""





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

     UpperCAmelCase_				:  int  = len(lowerCamelCase_  )

     UpperCAmelCase_				:  Dict  = [nodes[i].key for i in range(lowerCamelCase_  )]
     UpperCAmelCase_				:  Any  = [nodes[i].freq for i in range(lowerCamelCase_  )]

     # 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_				:  Optional[Any]  = [[freqs[i] if i == j else 0 for j in range(lowerCamelCase_  )] for i in range(lowerCamelCase_  )]
     # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
     # array
     UpperCAmelCase_				:  Any  = [[freqs[i] if i == j else 0 for j in range(lowerCamelCase_  )] for i in range(lowerCamelCase_  )]
     # stores tree roots that will be used later for constructing binary search tree
     UpperCAmelCase_				:  Optional[int]  = [[i if i == j else 0 for j in range(lowerCamelCase_  )] for i in range(lowerCamelCase_  )]

     for interval_length in range(2      ,	n + 1  ):
          for i in range(n - interval_length + 1  ):
               UpperCAmelCase_				:  Optional[Any]  = i + interval_length - 1

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

                    if dp[i][j] > cost:
                         UpperCAmelCase_				:  Dict  = cost
                         UpperCAmelCase_				:  Tuple  = r

     print('Binary search tree nodes:'  )
     for node in nodes:
          print(lowerCamelCase_  )

     print(F'''\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'''  )
     print_binary_search_tree(lowerCamelCase_      ,	lowerCamelCase_      ,	0      ,	n - 1      ,	-1      ,	lowerCamelCase_  )


def    _lowerCamelCase       ( ):



     """simple docstring"""





     UpperCAmelCase_				:  Any  = [Node(lowerCamelCase_      ,	randint(1      ,	50  )  ) for i in range(10      ,	0      ,	-1  )]
     find_optimal_binary_search_tree(lowerCamelCase_  )


if __name__ == "__main__":
 main()






