






'''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 :

      '''simple docstring'''





      def __init__(					self  ,		_UpperCAmelCase  ,		_UpperCAmelCase						):
             UpperCAmelCase__	:   Optional[int]												=	key
             UpperCAmelCase__	:   int												=	freq




      def __str__(					self						):
             return F"""Node(key={self.key}, freq={self.freq})"""






def  lowerCAmelCase__		(					a_  :     Dict			,						a_  :     Optional[int]			,						a_  :     str			,						a_  :     Dict			,						a_  :     int			,						a_  :     int			)   -> int:
       if i > j or i < 0 or j > len(a_			) - 1:
              return

       UpperCAmelCase__	:   str												=	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(a_			,						a_			,						a_			,						node - 1			,						key[node]			,						a_			)
       print_binary_search_tree(a_			,						a_			,						node + 1			,						a_			,						key[node]			,						a_			)






def  lowerCAmelCase__		(					a_  :     Optional[Any]			)   -> List[str]:
       nodes.sort(key=lambda a_			: node.key			)

       UpperCAmelCase__	:   List[Any]												=	len(a_			)

       UpperCAmelCase__	:   Union[str, Any]												=	[nodes[i].key for i in range(a_			)]
       UpperCAmelCase__	:   List[str]												=	[nodes[i].freq for i in range(a_			)]

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

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

                     UpperCAmelCase__	:   List[Any]												=	sys.maxsize  # set the value to "infinity"
                     UpperCAmelCase__	:   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
                            UpperCAmelCase__	:   Any												=	dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                            UpperCAmelCase__	:   int												=	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__	:   Dict												=	cost
                                   UpperCAmelCase__	:   Optional[int]												=	r

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

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






def  lowerCAmelCase__		(					)   -> Union[str, Any]:
       # A sample binary search tree
       UpperCAmelCase__	:   Any												=	[Node(a_			,						randint(1			,						5_0			)			) for i in range(1_0			,						0			,						-1			)]
       find_optimal_binary_search_tree(a_			)


if __name__ == "__main__":
  main()







'''simple docstring'''







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


UpperCamelCase_					=				{
    "configuration_flava": [
        "FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "FlavaConfig",
        "FlavaImageCodebookConfig",
        "FlavaImageConfig",
        "FlavaMultimodalConfig",
        "FlavaTextConfig",
    ],
}

try:
  if not is_vision_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase_					=				["FlavaFeatureExtractor"]
  UpperCamelCase_					=				["FlavaImageProcessor"]
  UpperCamelCase_					=				["FlavaProcessor"]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase_					=				[
      "FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST",
      "FlavaForPreTraining",
      "FlavaImageCodebook",
      "FlavaImageModel",
      "FlavaModel",
      "FlavaMultimodalModel",
      "FlavaPreTrainedModel",
      "FlavaTextModel",
  ]

if TYPE_CHECKING:
  from .configuration_flava import (
      FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP,
      FlavaConfig,
      FlavaImageCodebookConfig,
      FlavaImageConfig,
      FlavaMultimodalConfig,
      FlavaTextConfig,
  )

  try:
    if not is_vision_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .feature_extraction_flava import FlavaFeatureExtractor
    from .image_processing_flava import FlavaImageProcessor
    from .processing_flava import FlavaProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flava import (
        FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST,
        FlavaForPreTraining,
        FlavaImageCodebook,
        FlavaImageModel,
        FlavaModel,
        FlavaMultimodalModel,
        FlavaPreTrainedModel,
        FlavaTextModel,
    )

else:
  import sys

  UpperCamelCase_					=				_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)