
'''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 			lowerCAmelCase__ :



  '''simple docstring'''






  def __init__(self	:			Tuple						,			lowerCAmelCase_	:			Union[str, Any]						,			lowerCAmelCase_	:			Any     ) ->							Dict:
        snake_case_    							=				key
        snake_case_    							=				freq


  def __str__(self	:			Tuple     ) ->							Optional[Any]:
        return f'''Node(key={self.key}, freq={self.freq})'''

def 	snake_case_							(				_a  :				Any			,       _a  :				Dict			,       _a  :				List[str]			,       _a  :				Any			,       _a  :				Tuple			,       _a  :				List[str]      ):
      if i > j or i < 0 or j > len(SCREAMING_SNAKE_CASE__      ) - 1:
            return

      snake_case_    							=				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(SCREAMING_SNAKE_CASE__			,       SCREAMING_SNAKE_CASE__			,       SCREAMING_SNAKE_CASE__			,       node - 1			,       key[node]			,       SCREAMING_SNAKE_CASE__      )
      print_binary_search_tree(SCREAMING_SNAKE_CASE__			,       SCREAMING_SNAKE_CASE__			,       node + 1			,       SCREAMING_SNAKE_CASE__			,       key[node]			,       SCREAMING_SNAKE_CASE__      )
def 	snake_case_							(				_a  :				str      ):
      nodes.sort(key=lambda _a      : node.key      )

      snake_case_    							=				len(SCREAMING_SNAKE_CASE__      )

      snake_case_    							=				[nodes[i].key for i in range(SCREAMING_SNAKE_CASE__      )]
      snake_case_    							=				[nodes[i].freq for i in range(SCREAMING_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.
      snake_case_    							=				[[freqs[i] if i == j else 0 for j in range(SCREAMING_SNAKE_CASE__      )] for i in range(SCREAMING_SNAKE_CASE__      )]
      # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
      # array
      snake_case_    							=				[[freqs[i] if i == j else 0 for j in range(SCREAMING_SNAKE_CASE__      )] for i in range(SCREAMING_SNAKE_CASE__      )]
      # stores tree roots that will be used later for constructing binary search tree
      snake_case_    							=				[[i if i == j else 0 for j in range(SCREAMING_SNAKE_CASE__      )] for i in range(SCREAMING_SNAKE_CASE__      )]

      for interval_length in range(2			,       n + 1      ):
            for i in range(n - interval_length + 1      ):
                  snake_case_    							=				i + interval_length - 1

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

                        if dp[i][j] > cost:
                              snake_case_    							=				cost
                              snake_case_    							=				r

      print("Binary search tree nodes:"      )
      for node in nodes:
            print(SCREAMING_SNAKE_CASE__      )

      print(F'''\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'''      )
      print_binary_search_tree(SCREAMING_SNAKE_CASE__			,       SCREAMING_SNAKE_CASE__			,       0			,       n - 1			,       -1			,       SCREAMING_SNAKE_CASE__      )
def 	snake_case_							(				):
      # A sample binary search tree
      snake_case_    							=				[Node(SCREAMING_SNAKE_CASE__			,       randint(1			,       50      )      ) for i in range(10			,       0			,       -1      )]
      find_optimal_binary_search_tree(SCREAMING_SNAKE_CASE__      )


if __name__ == "__main__":
     main()








from typing import TYPE_CHECKING

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


__UpperCAmelCase			:  List[str]										=				{"configuration_levit": ["LEVIT_PRETRAINED_CONFIG_ARCHIVE_MAP", "LevitConfig", "LevitOnnxConfig"]}

try:
      if not is_vision_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase			:  Any										=				["LevitFeatureExtractor"]
      __UpperCAmelCase			:  Tuple										=				["LevitImageProcessor"]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __UpperCAmelCase			:  str										=				[
          "LEVIT_PRETRAINED_MODEL_ARCHIVE_LIST",
          "LevitForImageClassification",
          "LevitForImageClassificationWithTeacher",
          "LevitModel",
          "LevitPreTrainedModel",
      ]


if TYPE_CHECKING:
      from .configuration_levit import LEVIT_PRETRAINED_CONFIG_ARCHIVE_MAP, LevitConfig, LevitOnnxConfig

      try:
            if not is_vision_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .feature_extraction_levit import LevitFeatureExtractor
            from .image_processing_levit import LevitImageProcessor

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_levit import (
                LEVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
                LevitForImageClassification,
                LevitForImageClassificationWithTeacher,
                LevitModel,
                LevitPreTrainedModel,
            )
else:
      import sys

      __UpperCAmelCase			:  Union[str, Any]										=				_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






