

# 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 							a__							:







  """simple docstring"""




  def __init__(      self     :			str					,					UpperCAmelCase__     :			List[str]					,					UpperCAmelCase__     :			Optional[Any]		)       ->List[Any]:
        """simple docstring"""







        SCREAMING_SNAKE_CASE			:   List[str]	  = key
        SCREAMING_SNAKE_CASE			:   int	  = freq




  def __str__(      self     :			List[str]		)       ->Union[str, Any]:
        """simple docstring"""







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






def        __lowercase   (  _A    ,     _A    ,     _A    ,     _A    ,     _A    ,     _A      )  ->    int:
      if i > j or i < 0 or j > len(_A      ) - 1:
            return

      SCREAMING_SNAKE_CASE			:   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(_A    ,     _A    ,     _A    ,     node - 1    ,     key[node]    ,     _A      )
      print_binary_search_tree(_A    ,     _A    ,     node + 1    ,     _A    ,     key[node]    ,     _A      )






def        __lowercase   (  _A      )  ->    Optional[Any]:
      nodes.sort(key=lambda _A      : node.key      )

      SCREAMING_SNAKE_CASE			:   Optional[int]	  = len(_A      )

      SCREAMING_SNAKE_CASE			:   Optional[int]	  = [nodes[i].key for i in range(_A      )]
      SCREAMING_SNAKE_CASE			:   Optional[Any]	  = [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			:   Dict	  = [[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			:   List[str]	  = [[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			:   Optional[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      ):
                  SCREAMING_SNAKE_CASE			:   int	  = i + interval_length - 1

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

                        if dp[i][j] > cost:
                              SCREAMING_SNAKE_CASE			:   Tuple	  = cost
                              SCREAMING_SNAKE_CASE			:   Any	  = 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        __lowercase   (  )  ->    List[Any]:
      # A sample binary search tree
      SCREAMING_SNAKE_CASE			:   int	  = [Node(_A    ,     randint(1    ,     50      )      ) for i in range(10    ,     0    ,     -1      )]
      find_optimal_binary_search_tree(_A      )


if __name__ == "__main__":
  main()







import logging
from pathlib import Path

import numpy as np
import pytorch_lightning as pl
import torch
from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
from pytorch_lightning.utilities import rank_zero_only

from utils import save_json






def        __lowercase   (  _A      )  ->    Dict:
      SCREAMING_SNAKE_CASE			:   Dict	  = filter(lambda _A      : p.requires_grad    ,     model.parameters()      )
      SCREAMING_SNAKE_CASE			:   Optional[int]	  = sum([np.prod(p.size()      ) for p in model_parameters]      )
      return params


UpperCAmelCase__			:  List[Any]					     =     logging.getLogger(__name__)







class 							a__							( pl.Callback							):







  """simple docstring"""




  def 			_lowercase   (      self     :			List[Any]					,					UpperCAmelCase__     :			str					,					UpperCAmelCase__     :			Any		)       ->Optional[int]:
        """simple docstring"""







        SCREAMING_SNAKE_CASE			:   List[str]	  = {f"lr_group_{i}": param["""lr"""] for i, param in enumerate(pl_module.trainer.optimizers[0].param_groups		)}
        pl_module.logger.log_metrics(UpperCAmelCase__		)


  @rank_zero_only
  def 			_lowercase   (      self     :			List[Any]					,					UpperCAmelCase__     :			pl.Trainer					,					UpperCAmelCase__     :			pl.LightningModule					,					UpperCAmelCase__     :			str					,					UpperCAmelCase__     :			Tuple=True		)       ->None:
        """simple docstring"""







        logger.info(f"***** {type_path} results at step {trainer.global_step:05d} *****"		)
        SCREAMING_SNAKE_CASE			:   Union[str, Any]	  = trainer.callback_metrics
        trainer.logger.log_metrics({k: v for k, v in metrics.items() if k not in ["""log""", """progress_bar""", """preds"""]}		)
        # Log results
        SCREAMING_SNAKE_CASE			:   Union[str, Any]	  = Path(pl_module.hparams.output_dir		)
        if type_path == "test":
              SCREAMING_SNAKE_CASE			:   Optional[int]	  = od / """test_results.txt"""
              SCREAMING_SNAKE_CASE			:   int	  = od / """test_generations.txt"""
        else:
              # this never gets hit. I prefer not to save intermediate generations, and results are in metrics.json
              # If people want this it will be easy enough to add back.
              SCREAMING_SNAKE_CASE			:   Any	  = od / f"{type_path}_results/{trainer.global_step:05d}.txt"
              SCREAMING_SNAKE_CASE			:   int	  = od / f"{type_path}_generations/{trainer.global_step:05d}.txt"
              results_file.parent.mkdir(exist_ok=UpperCAmelCase__		)
              generations_file.parent.mkdir(exist_ok=UpperCAmelCase__		)
        with open(UpperCAmelCase__					,					"""a+"""		) as writer:
              for key in sorted(UpperCAmelCase__		):
                    if key in ["log", "progress_bar", "preds"]:
                          continue
                    SCREAMING_SNAKE_CASE			:   Optional[int]	  = metrics[key]
                    if isinstance(UpperCAmelCase__					,					torch.Tensor		):
                          SCREAMING_SNAKE_CASE			:   Optional[int]	  = val.item()
                    SCREAMING_SNAKE_CASE			:   List[str]	  = f"{key}: {val:.6f}\n"
                    writer.write(UpperCAmelCase__		)

        if not save_generations:
              return

        if "preds" in metrics:
              SCREAMING_SNAKE_CASE			:   Optional[int]	  = """\n""".join(metrics["""preds"""]		)
              generations_file.open("""w+"""		).write(UpperCAmelCase__		)


  @rank_zero_only
  def 			_lowercase   (      self     :			Optional[int]					,					UpperCAmelCase__     :			Optional[int]					,					UpperCAmelCase__     :			Union[str, Any]		)       ->int:
        """simple docstring"""







        try:
              SCREAMING_SNAKE_CASE			:   int	  = pl_module.model.model.num_parameters()
        except AttributeError:
              SCREAMING_SNAKE_CASE			:   Optional[Any]	  = pl_module.model.num_parameters()

        SCREAMING_SNAKE_CASE			:   Dict	  = count_trainable_parameters(UpperCAmelCase__		)
        # mp stands for million parameters
        trainer.logger.log_metrics({"""n_params""": npars, """mp""": npars / 1e6, """grad_mp""": n_trainable_pars / 1e6}		)


  @rank_zero_only
  def 			_lowercase   (      self     :			str					,					UpperCAmelCase__     :			pl.Trainer					,					UpperCAmelCase__     :			pl.LightningModule		)       ->Optional[int]:
        """simple docstring"""







        save_json(pl_module.metrics					,					pl_module.metrics_save_path		)
        return self._write_logs(UpperCAmelCase__					,					UpperCAmelCase__					,					"""test"""		)




  @rank_zero_only
  def 			_lowercase   (      self     :			List[Any]					,					UpperCAmelCase__     :			pl.Trainer					,					UpperCAmelCase__     :			List[Any]		)       ->Dict:
        """simple docstring"""







        save_json(pl_module.metrics					,					pl_module.metrics_save_path		)
        # Uncommenting this will save val generations
        # return self._write_logs(trainer, pl_module, "valid")






def        __lowercase   (  _A    ,     _A    ,     _A=1    ,     _A=False      )  ->    Tuple:
      if metric == "rouge2":
            SCREAMING_SNAKE_CASE			:   Union[str, Any]	  = """{val_avg_rouge2:.4f}-{step_count}"""
      elif metric == "bleu":
            SCREAMING_SNAKE_CASE			:   Tuple	  = """{val_avg_bleu:.4f}-{step_count}"""
      elif metric == "loss":
            SCREAMING_SNAKE_CASE			:   Any	  = """{val_avg_loss:.4f}-{step_count}"""
      else:
            raise NotImplementedError(
                F"seq2seq callbacks only support rouge2, bleu and loss, got {metric}, You can make your own by adding to"
                """ this function."""      )

      SCREAMING_SNAKE_CASE			:   Tuple	  = ModelCheckpoint(
          dirpath=_A    ,     filename=_A    ,     monitor=F"val_{metric}"    ,     mode="""min""" if """loss""" in metric else """max"""    ,     save_top_k=_A    ,     )
      return checkpoint_callback







def        __lowercase   (  _A    ,     _A      )  ->    Optional[int]:
      return EarlyStopping(
          monitor=F"val_{metric}"    ,     mode="""min""" if """loss""" in metric else """max"""    ,     patience=_A    ,     verbose=_A    ,     )




