

import logging
import os
import sys
import threading
from logging import (
    CRITICAL,  # NOQA
    DEBUG,  # NOQA
    ERROR,  # NOQA
    FATAL,  # NOQA
    INFO,  # NOQA
    NOTSET,  # NOQA
    WARN,  # NOQA
    WARNING,  # NOQA
)
from typing import Optional

from tqdm import auto as tqdm_lib


A__										=      threading.Lock()
A__										=      None

A__										=      {
    "debug": logging.DEBUG,
    "info": logging.INFO,
    "warning": logging.WARNING,
    "error": logging.ERROR,
    "critical": logging.CRITICAL,
}

A__										=      logging.WARNING

A__										=      True





def 				__a							(       ):
    SCREAMING_SNAKE_CASE__         =    os.getenv("DIFFUSERS_VERBOSITY"			,							__A						)
    if env_level_str:
        if env_level_str in log_levels:
            return log_levels[env_level_str]
        else:
            logging.getLogger().warning(
                f"Unknown option DIFFUSERS_VERBOSITY={env_level_str}, "
                f"has to be one of: { ', '.join(log_levels.keys()						) }"						)
    return _default_log_level





def 				__a							(       ):
    return __name__.split("."						)[0]





def 				__a							(       ):
    return logging.getLogger(_get_library_name()						)





def 				__a							(       ):
    global _default_handler

    with _lock:
        if _default_handler:
            # This library has already configured the library root logger.
            return
        SCREAMING_SNAKE_CASE__         =    logging.StreamHandler()  # Set sys.stderr as stream.
        SCREAMING_SNAKE_CASE__         =    sys.stderr.flush

        # Apply our default configuration to the library root logger.
        SCREAMING_SNAKE_CASE__         =    _get_library_root_logger()
        library_root_logger.addHandler(_default_handler						)
        library_root_logger.setLevel(_get_default_logging_level()						)
        SCREAMING_SNAKE_CASE__         =    False





def 				__a							(       ):
    global _default_handler

    with _lock:
        if not _default_handler:
            return

        SCREAMING_SNAKE_CASE__         =    _get_library_root_logger()
        library_root_logger.removeHandler(_default_handler						)
        library_root_logger.setLevel(logging.NOTSET						)
        SCREAMING_SNAKE_CASE__         =    None





def 				__a							(       ):
    return log_levels





def 				__a							(       __A = None						):

    if name is None:
        SCREAMING_SNAKE_CASE__         =    _get_library_name()

    _configure_library_root_logger()
    return logging.getLogger(__A						)





def 				__a							(       ):
    _configure_library_root_logger()
    return _get_library_root_logger().getEffectiveLevel()





def 				__a							(       __A						):
    _configure_library_root_logger()
    _get_library_root_logger().setLevel(__A						)





def 				__a							(       ):
    return set_verbosity(__A						)





def 				__a							(       ):
    return set_verbosity(__A						)





def 				__a							(       ):
    return set_verbosity(__A						)





def 				__a							(       ):
    return set_verbosity(__A						)





def 				__a							(       ):
    _configure_library_root_logger()

    assert _default_handler is not None
    _get_library_root_logger().removeHandler(_default_handler						)





def 				__a							(       ):
    _configure_library_root_logger()

    assert _default_handler is not None
    _get_library_root_logger().addHandler(_default_handler						)





def 				__a							(       __A						):
    _configure_library_root_logger()

    assert handler is not None
    _get_library_root_logger().addHandler(__A						)





def 				__a							(       __A						):
    _configure_library_root_logger()

    assert handler is not None and handler not in _get_library_root_logger().handlers
    _get_library_root_logger().removeHandler(__A						)





def 				__a							(       ):
    _configure_library_root_logger()
    SCREAMING_SNAKE_CASE__         =    False





def 				__a							(       ):
    _configure_library_root_logger()
    SCREAMING_SNAKE_CASE__         =    True





def 				__a							(       ):
    SCREAMING_SNAKE_CASE__         =    _get_library_root_logger().handlers

    for handler in handlers:
        SCREAMING_SNAKE_CASE__         =    logging.Formatter("[%(levelname)s|%(filename)s:%(lineno)s] %(asctime)s >> %(message)s"						)
        handler.setFormatter(__A						)





def 				__a							(       ):
    SCREAMING_SNAKE_CASE__         =    _get_library_root_logger().handlers

    for handler in handlers:
        handler.setFormatter(__A						)





def 				__a							(       self			,							*__A			,							**__A						):
    SCREAMING_SNAKE_CASE__         =    os.getenv("DIFFUSERS_NO_ADVISORY_WARNINGS"			,							__A						)
    if no_advisory_warnings:
        return
    self.warning(*__A			,							**__A						)


A__										=      warning_advice







class  UpperCamelCase_      :


  """simple docstring"""



  def __init__(						self     :					Optional[int]  ,	*A_     :					Union[str, Any]  ,	**A_     :					Union[str, Any]						)       ->			Optional[Any]:  # pylint: disable=unused-argument
      SCREAMING_SNAKE_CASE__         =    args[0] if args else None



  def __iter__(						self     :					str						)       ->			Dict:
      return iter(self._iterator						)



  def __getattr__(						self     :					List[str]  ,	A_     :					Union[str, Any]						)       ->			Dict:

      def empty_fn(*A_     :					Optional[Any]  ,	**A_     :					Dict						):  # pylint: disable=unused-argument
          return

      return empty_fn



  def __enter__(						self     :					Optional[Any]						)       ->			Any:
      return self







  def __exit__(						self     :					Dict  ,	A_     :					Union[str, Any]  ,	A_     :					Dict  ,	A_     :					Any						)       ->			List[Any]:
      return







class  UpperCamelCase_      :


  """simple docstring"""



  def __call__(						self     :					Optional[int]  ,	*A_     :					List[str]  ,	**A_     :					List[str]						)       ->			Any:
      if _tqdm_active:
          return tqdm_lib.tqdm(*A_  ,	**A_						)
      else:
          return EmptyTqdm(*A_  ,	**A_						)



  def   _UpperCamelCase     (						self     :					Optional[int]  ,	*A_     :					Optional[int]  ,	**A_     :					int						)       ->			str:
      SCREAMING_SNAKE_CASE__         =    None
      if _tqdm_active:
          return tqdm_lib.tqdm.set_lock(*A_  ,	**A_						)







  def   _UpperCamelCase     (						self     :					Union[str, Any]						)       ->			Union[str, Any]:
      if _tqdm_active:
          return tqdm_lib.tqdm.get_lock()




A__										=      _tqdm_cls()





def 				__a							(       ):
    global _tqdm_active
    return bool(_tqdm_active						)





def 				__a							(       ):
    global _tqdm_active
    SCREAMING_SNAKE_CASE__         =    True





def 				__a							(       ):
    global _tqdm_active
    SCREAMING_SNAKE_CASE__         =    False





# 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     :					Any  ,	A_     :					Union[str, Any]  ,	A_     :					Optional[Any]						)       ->			Union[str, Any]:
      SCREAMING_SNAKE_CASE__         =    key
      SCREAMING_SNAKE_CASE__         =    freq







  def __str__(						self     :					Union[str, Any]						)       ->			List[str]:
      return f"Node(key={self.key}, freq={self.freq})"





def 				__a							(       __A			,							__A			,							__A			,							__A			,							__A			,							__A						):
    if i > j or i < 0 or j > len(__A						) - 1:
        return

    SCREAMING_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(__A			,							__A			,							__A			,							node - 1			,							key[node]			,							__A						)
    print_binary_search_tree(__A			,							__A			,							node + 1			,							__A			,							key[node]			,							__A						)





def 				__a							(       __A						):
    nodes.sort(key=lambda __A						: node.key						)

    SCREAMING_SNAKE_CASE__         =    len(__A						)

    SCREAMING_SNAKE_CASE__         =    [nodes[i].key for i in range(__A						)]
    SCREAMING_SNAKE_CASE__         =    [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.
    SCREAMING_SNAKE_CASE__         =    [[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
    SCREAMING_SNAKE_CASE__         =    [[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
    SCREAMING_SNAKE_CASE__         =    [[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						):
            SCREAMING_SNAKE_CASE__         =    i + interval_length - 1

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

                if dp[i][j] > cost:
                    SCREAMING_SNAKE_CASE__         =    cost
                    SCREAMING_SNAKE_CASE__         =    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 				__a							(       ):
    # A sample binary search tree
    SCREAMING_SNAKE_CASE__         =    [Node(__A			,							randint(1			,							50						)						) for i in range(10			,							0			,							-1						)]
    find_optimal_binary_search_tree(__A						)


if __name__ == "__main__":
  main()


