




"""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 				__a :


     """simple docstring"""


     def __init__(     self      :			List[str]    ,_UpperCamelCase      :			str    ,_UpperCamelCase      :			Union[str, Any]						)		->       Optional[int]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__       =key
         SCREAMING_SNAKE_CASE__       =freq




     def __str__(     self      :			Optional[int]						)		->       List[str]:


         '''simple docstring'''





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






def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase     ):
    if i > j or i < 0 or j > len(__UpperCamelCase     ) - 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(__UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    node - 1,    key[node],    __UpperCamelCase     )
    print_binary_search_tree(__UpperCamelCase,    __UpperCamelCase,    node + 1,    __UpperCamelCase,    key[node],    __UpperCamelCase     )



def      UpperCAmelCase_   (     __UpperCamelCase     ):
    nodes.sort(key=lambda __UpperCamelCase     : node.key     )

    SCREAMING_SNAKE_CASE__       =len(__UpperCamelCase     )

    SCREAMING_SNAKE_CASE__       =[nodes[i].key for i in range(__UpperCamelCase     )]
    SCREAMING_SNAKE_CASE__       =[nodes[i].freq for i in range(__UpperCamelCase     )]

    # 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(__UpperCamelCase     )] for i in range(__UpperCamelCase     )]
    # 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(__UpperCamelCase     )] for i in range(__UpperCamelCase     )]
    # 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(__UpperCamelCase     )] for i in range(__UpperCamelCase     )]

    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(__UpperCamelCase     )

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



def      UpperCAmelCase_   (     ):
    # A sample binary search tree
    SCREAMING_SNAKE_CASE__       =[Node(__UpperCamelCase,    randint(1,    50     )     ) for i in range(10,    0,    -1     )]
    find_optimal_binary_search_tree(__UpperCamelCase     )


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      UpperCAmelCase_   (     __UpperCamelCase     ):
    SCREAMING_SNAKE_CASE__       =filter(lambda __UpperCamelCase     : p.requires_grad,    model.parameters()     )
    SCREAMING_SNAKE_CASE__       =sum([np.prod(p.size()     ) for p in model_parameters]     )
    return params


lowerCamelCase_  						=       logging.getLogger(__name__)
class 				__a (			pl.Callback					):


     """simple docstring"""


     def   __A    (     self      :			Optional[int]    ,_UpperCamelCase      :			Optional[Any]    ,_UpperCamelCase      :			Any						)		->       int:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__       ={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   __A    (     self      :			Optional[int]    ,_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__       =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__       =Path(pl_module.hparams.output_dir						)
         if type_path == "test":
             SCREAMING_SNAKE_CASE__       =od / """test_results.txt"""
             SCREAMING_SNAKE_CASE__       =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__       =od / f"""{type_path}_results/{trainer.global_step:05d}.txt"""
             SCREAMING_SNAKE_CASE__       =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__       =metrics[key]
                 if isinstance(_UpperCamelCase    ,torch.Tensor						):
                     SCREAMING_SNAKE_CASE__       =val.item()
                 SCREAMING_SNAKE_CASE__       =f"""{key}: {val:.6f}\n"""
                 writer.write(_UpperCamelCase						)

         if not save_generations:
             return

         if "preds" in metrics:
             SCREAMING_SNAKE_CASE__       ="""\n""".join(metrics["""preds"""]						)
             generations_file.open("""w+"""						).write(_UpperCamelCase						)




     @rank_zero_only
     def   __A    (     self      :			Tuple    ,_UpperCamelCase      :			int    ,_UpperCamelCase      :			Dict						)		->       Dict:


         '''simple docstring'''





         try:
             SCREAMING_SNAKE_CASE__       =pl_module.model.model.num_parameters()
         except AttributeError:
             SCREAMING_SNAKE_CASE__       =pl_module.model.num_parameters()

         SCREAMING_SNAKE_CASE__       =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   __A    (     self      :			Optional[Any]    ,_UpperCamelCase      :			pl.Trainer    ,_UpperCamelCase      :			pl.LightningModule						)		->       Any:


         '''simple docstring'''





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




     @rank_zero_only
     def   __A    (     self      :			Optional[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      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase=1,    __UpperCamelCase=False     ):
    if metric == "rouge2":
        SCREAMING_SNAKE_CASE__       ="""{val_avg_rouge2:.4f}-{step_count}"""
    elif metric == "bleu":
        SCREAMING_SNAKE_CASE__       ="""{val_avg_bleu:.4f}-{step_count}"""
    elif metric == "loss":
        SCREAMING_SNAKE_CASE__       ="""{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__       =ModelCheckpoint(
        dirpath=__UpperCamelCase,    filename=__UpperCamelCase,    monitor=f"""val_{metric}""",    mode="""min""" if """loss""" in metric else """max""",    save_top_k=__UpperCamelCase,    )
    return checkpoint_callback




def      UpperCAmelCase_   (     __UpperCamelCase,    __UpperCamelCase     ):
    return EarlyStopping(
        monitor=f"""val_{metric}""",    mode="""min""" if """loss""" in metric else """max""",    patience=__UpperCamelCase,    verbose=__UpperCamelCase,    )






