


# 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			,       __SCREAMING_SNAKE_CASE			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              UpperCamelCase     :						Optional[Any] 						=		key
              UpperCamelCase     :						List[str] 						=		freq






       def __str__(  self    ):




              """simple docstring"""




              return f"""Node(key={self.key}, freq={self.freq})"""




def   a						(				SCREAMING_SNAKE_CASE_   :		Dict				,      SCREAMING_SNAKE_CASE_   :		Tuple				,      SCREAMING_SNAKE_CASE_   :		int				,      SCREAMING_SNAKE_CASE_   :		Dict				,      SCREAMING_SNAKE_CASE_   :		int				,      SCREAMING_SNAKE_CASE_   :		List[Any]							):






       """simple docstring"""





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

       UpperCamelCase     :						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(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   a						(				SCREAMING_SNAKE_CASE_   :		Any							):






       """simple docstring"""





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

       UpperCamelCase     :						List[Any] 						=		len(SCREAMING_SNAKE_CASE_							)

       UpperCamelCase     :						Tuple 						=		[nodes[i].key for i in range(SCREAMING_SNAKE_CASE_							)]
       UpperCamelCase     :						Optional[Any] 						=		[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.
       UpperCamelCase     :						Tuple 						=		[[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
       UpperCamelCase     :						Tuple 						=		[[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
       UpperCamelCase     :						Optional[Any] 						=		[[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							):
                     UpperCamelCase     :						Optional[int] 						=		i + interval_length - 1

                     UpperCamelCase     :						Dict 						=		sys.maxsize  # set the value to "infinity"
                     UpperCamelCase     :						List[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     :						List[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     :						Dict 						=		left + total[i][j] + right

                            if dp[i][j] > cost:
                                   UpperCamelCase     :						List[Any] 						=		cost
                                   UpperCamelCase     :						Tuple 						=		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   a						(				):






       """simple docstring"""





       UpperCamelCase     :						str 						=		[Node(SCREAMING_SNAKE_CASE_				,      randint(1				,      5_0							)							) for i in range(1_0				,      0				,      -1							)]
       find_optimal_binary_search_tree(SCREAMING_SNAKE_CASE_							)


if __name__ == "__main__":
  main()





import os

from apache_beam.io.filesystems import FileSystems
from apache_beam.pipeline import Pipeline

from .logging import get_logger


__UpperCAmelCase			:			Optional[Any]			      =					2 << 20  # 2mb
__UpperCAmelCase			:			List[Any]			      =					get_logger(__name__)



class  UpperCAmelCase_						(				_a):
       '''simple docstring'''






       def 			_lowercase (  self    ):




              """simple docstring"""




              UpperCamelCase     :						Optional[Any] 						=		self._options.get_all_options().get('''runner'''    )
              return runner in [None, "DirectRunner", "PortableRunner"]




def   a						(				SCREAMING_SNAKE_CASE_   :		str				,      SCREAMING_SNAKE_CASE_   :		int				,      SCREAMING_SNAKE_CASE_   :		Optional[Any]=False							):






       """simple docstring"""





       UpperCamelCase     :						int 						=		FileSystems
       if fs.exists(SCREAMING_SNAKE_CASE_							):
              if force_upload:
                     logger.info(F"""Remote path already exist: {remote_file_path}. Overwriting it as force_upload=True."""							)
              else:
                     logger.info(F"""Remote path already exist: {remote_file_path}. Skipping it as force_upload=False."""							)
                     return
       with fs.create(SCREAMING_SNAKE_CASE_							) as remote_file:
              with open(SCREAMING_SNAKE_CASE_				,      '''rb'''							) as local_file:
                     UpperCamelCase     :						List[str] 						=		local_file.read(SCREAMING_SNAKE_CASE_							)
                     while chunk:
                            remote_file.write(SCREAMING_SNAKE_CASE_							)
                            UpperCamelCase     :						Any 						=		local_file.read(SCREAMING_SNAKE_CASE_							)


def   a						(				SCREAMING_SNAKE_CASE_   :		str				,      SCREAMING_SNAKE_CASE_   :		Optional[Any]				,      SCREAMING_SNAKE_CASE_   :		List[str]=False							):






       """simple docstring"""





       UpperCamelCase     :						List[Any] 						=		FileSystems
       if os.path.exists(SCREAMING_SNAKE_CASE_							):
              if force_download:
                     logger.info(F"""Local path already exist: {remote_file_path}. Overwriting it as force_upload=True."""							)
              else:
                     logger.info(F"""Local path already exist: {remote_file_path}. Skipping it as force_upload=False."""							)
                     return
       with fs.open(SCREAMING_SNAKE_CASE_							) as remote_file:
              with open(SCREAMING_SNAKE_CASE_				,      '''wb'''							) as local_file:
                     UpperCamelCase     :						List[str] 						=		remote_file.read(SCREAMING_SNAKE_CASE_							)
                     while chunk:
                            local_file.write(SCREAMING_SNAKE_CASE_							)
                            UpperCamelCase     :						str 						=		remote_file.read(SCREAMING_SNAKE_CASE_							)

