



"""simple docstring"""

from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

lowercase__					:						int												=			TypeVar('''T''')




def __lowercase    (							_a					):
    return (position - 1) // 2




def __lowercase    (							_a					):
    return (2 * position) + 1




def __lowercase    (							_a					):
    return (2 * position) + 2




class  _UpperCAmelCase (    Generic[T]):

 def __init__(  self	: Optional[Any]       ):
     snake_case_				:  list[tuple[T, int]]       =			[]
     snake_case_				:  dict[T, int]       =			{}
     snake_case_				:  int       =			0

 def __len__(  self	: List[Any]       ):
     return self.elements

 def __repr__(  self	: Optional[int]       ):
     return str(self.heap       )

 def 		_snake_case      (  self	: Any       ):
     # Check if the priority queue is empty
     return self.elements == 0

 def 		_snake_case      (  self	: Tuple						,  lowercase_	: T						,  lowercase_	: int       ):
     # Add an element with given priority to the queue
     self.heap.append((elem, weight)       )
     snake_case_				:  Union[str, Any]       =			self.elements
     self.elements += 1
     self._bubble_up(lowercase_       )

 def 		_snake_case      (  self	: int       ):
     # Remove and return the element with lowest weight (highest priority)
     if self.elements > 1:
         self._swap_nodes(0						,  self.elements - 1       )
     snake_case_				:  List[str]       =			self.heap.pop()
     del self.position_map[elem]
     self.elements -= 1
     if self.elements > 0:
         snake_case_				:  Optional[Any]       =			self.heap[0]
         self._bubble_down(lowercase_       )
     return elem

 def 		_snake_case      (  self	: Tuple						,  lowercase_	: T						,  lowercase_	: int       ):
     # Update the weight of the given key
     snake_case_				:  Tuple       =			self.position_map[elem]
     snake_case_				:  Optional[Any]       =			(elem, weight)
     if position > 0:
         snake_case_				:  Optional[int]       =			get_parent_position(lowercase_       )
         snake_case_				:  Dict       =			self.heap[parent_position]
         if parent_weight > weight:
             self._bubble_up(lowercase_       )
         else:
             self._bubble_down(lowercase_       )
     else:
         self._bubble_down(lowercase_       )

 def 		_snake_case      (  self	: Optional[Any]						,  lowercase_	: T       ):
     # Place a node at the proper position (upward movement) [to be used internally
     # only]
     snake_case_				:  List[str]       =			self.position_map[elem]
     if curr_pos == 0:
         return None
     snake_case_				:  Optional[Any]       =			get_parent_position(lowercase_       )
     snake_case_				:  Any       =			self.heap[curr_pos]
     snake_case_				:  Tuple       =			self.heap[parent_position]
     if parent_weight > weight:
         self._swap_nodes(lowercase_						,  lowercase_       )
         return self._bubble_up(lowercase_       )
     return None

 def 		_snake_case      (  self	: Any						,  lowercase_	: T       ):
     # Place a node at the proper position (downward movement) [to be used
     # internally only]
     snake_case_				:  List[Any]       =			self.position_map[elem]
     snake_case_				:  Tuple       =			self.heap[curr_pos]
     snake_case_				:  Tuple       =			get_child_left_position(lowercase_       )
     snake_case_				:  Dict       =			get_child_right_position(lowercase_       )
     if child_left_position < self.elements and child_right_position < self.elements:
         snake_case_				:  Dict       =			self.heap[child_left_position]
         snake_case_				:  List[str]       =			self.heap[child_right_position]
         if child_right_weight < child_left_weight and child_right_weight < weight:
             self._swap_nodes(lowercase_						,  lowercase_       )
             return self._bubble_down(lowercase_       )
     if child_left_position < self.elements:
         snake_case_				:  str       =			self.heap[child_left_position]
         if child_left_weight < weight:
             self._swap_nodes(lowercase_						,  lowercase_       )
             return self._bubble_down(lowercase_       )
     else:
         return None
     if child_right_position < self.elements:
         snake_case_				:  Union[str, Any]       =			self.heap[child_right_position]
         if child_right_weight < weight:
             self._swap_nodes(lowercase_						,  lowercase_       )
             return self._bubble_down(lowercase_       )
     return None






 def 		_snake_case      (  self	: str						,  lowercase_	: int						,  lowercase_	: int       ):
     # Swap the nodes at the given positions
     snake_case_				:  Any       =			self.heap[nodea_pos][0]
     snake_case_				:  Tuple       =			self.heap[nodea_pos][0]
     snake_case_				:  List[Any]       =			(
         self.heap[nodea_pos],
         self.heap[nodea_pos],
     )
     snake_case_				:  Optional[Any]       =			nodea_pos
     snake_case_				:  int       =			nodea_pos





class  _UpperCAmelCase (    Generic[T]):

 def __init__(  self	: Union[str, Any]       ):
     snake_case_				:  dict[T, dict[T, int]]       =			{}
     snake_case_				:  int       =			0

 def __repr__(  self	: Tuple       ):
     return str(self.connections       )

 def __len__(  self	: int       ):
     return self.nodes

 def 		_snake_case      (  self	: Union[str, Any]						,  lowercase_	: T       ):
     # Add a node in the graph if it is not in the graph
     if node not in self.connections:
         snake_case_				:  List[str]       =			{}
         self.nodes += 1






 def 		_snake_case      (  self	: Any						,  lowercase_	: T						,  lowercase_	: T						,  lowercase_	: int       ):
     # Add an edge between 2 nodes in the graph
     self.add_node(lowercase_       )
     self.add_node(lowercase_       )
     snake_case_				:  Optional[Any]       =			weight
     snake_case_				:  Optional[int]       =			weight





def __lowercase    (							_a	,    ):
    snake_case_				:  dict[T, int]       =			{node: maxsize for node in graph.connections}
    snake_case_				:  dict[T, T | None]       =			{node: None for node in graph.connections}

    snake_case_				:  MinPriorityQueue[T]       =			MinPriorityQueue()
    for node, weight in dist.items():
        priority_queue.push(_a	,    _a					)

    if priority_queue.is_empty():
        return dist, parent

    # initialization
    snake_case_				:  Dict       =			priority_queue.extract_min()
    snake_case_				:  Dict       =			0
    for neighbour in graph.connections[node]:
        if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
            snake_case_				:  str       =			dist[node] + graph.connections[node][neighbour]
            priority_queue.update_key(_a	,    dist[neighbour]					)
            snake_case_				:  Tuple       =			node

    # running prim's algorithm
    while not priority_queue.is_empty():
        snake_case_				:  int       =			priority_queue.extract_min()
        for neighbour in graph.connections[node]:
            if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
                snake_case_				:  Union[str, Any]       =			dist[node] + graph.connections[node][neighbour]
                priority_queue.update_key(_a	,    dist[neighbour]					)
                snake_case_				:  Any       =			node
    return dist, parent










"""simple docstring"""

import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
     import torch_xla.core.xla_model as xm
     import torch_xla.debug.metrics as met




class  _UpperCAmelCase (    lowerCAmelCase__):

 def __init__(  self	: List[Any]						,  *lowercase_	: List[Any]						,  lowercase_	: Optional[Any]=None						,  lowercase_	: Tuple=None						,  **lowercase_	: Union[str, Any]       ):
     super().__init__(*lowercase_						,  **lowercase_       )
     snake_case_				:  str       =			eval_examples
     snake_case_				:  Optional[Any]       =			post_process_function

 def 		_snake_case      (  self	: Union[str, Any]						,  lowercase_	: Optional[Dataset] = None						,  lowercase_	: str=None						,  lowercase_	: Optional[List[str]] = None						,  lowercase_	: str = "eval"						,  **lowercase_	: Dict						,  ):
     snake_case_				:  int       =			gen_kwargs.copy()
     snake_case_				:  Dict       =			(
         gen_kwargs['''max_length'''] if gen_kwargs.get('''max_length'''       ) is not None else self.args.generation_max_length
     )
     snake_case_				:  Tuple       =			(
         gen_kwargs['''num_beams'''] if gen_kwargs.get('''num_beams'''       ) is not None else self.args.generation_num_beams
     )
     snake_case_				:  Optional[Any]       =			gen_kwargs

     snake_case_				:  Optional[int]       =			self.eval_dataset if eval_dataset is None else eval_dataset
     snake_case_				:  Optional[Any]       =			self.get_eval_dataloader(lowercase_       )
     snake_case_				:  Dict       =			self.eval_examples if eval_examples is None else eval_examples

     # Temporarily disable metric computation, we will do it in the loop here.
     snake_case_				:  Optional[int]       =			self.compute_metrics
     snake_case_				:  str       =			None
     snake_case_				:  int       =			time.time()
     snake_case_				:  Any       =			self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
     try:
         snake_case_				:  str       =			eval_loop(
             lowercase_						,  description='''Evaluation'''						,  prediction_loss_only=True if compute_metrics is None else None						,  ignore_keys=lowercase_						,  metric_key_prefix=lowercase_						,  )
     finally:
         snake_case_				:  Optional[int]       =			compute_metrics
     snake_case_				:  Dict       =			self.args.eval_batch_size * self.args.world_size
     if f"{metric_key_prefix}_jit_compilation_time" in output.metrics:
         start_time += output.metrics[f"{metric_key_prefix}_jit_compilation_time"]
     output.metrics.update(
         speed_metrics(
             lowercase_						,  lowercase_						,  num_samples=output.num_samples						,  num_steps=math.ceil(output.num_samples / total_batch_size       )						,  )       )

     if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
         # Only the main node write the results by default
         snake_case_				:  Tuple       =			self.post_process_function(lowercase_						,  lowercase_						,  lowercase_       )
         snake_case_				:  Optional[int]       =			self.compute_metrics(lowercase_       )

         # Prefix all keys with metric_key_prefix + '_'
         for key in list(metrics.keys()       ):
             if not key.startswith(f"{metric_key_prefix}_"       ):
                 snake_case_				:  int       =			metrics.pop(lowercase_       )

         metrics.update(output.metrics       )
     else:
         snake_case_				:  Tuple       =			output.metrics

     if self.args.should_log:
         # Only the main node log the results by default
         self.log(lowercase_       )

     if self.args.tpu_metrics_debug or self.args.debug:
         # tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
         xm.master_print(met.metrics_report()       )

     snake_case_				:  str       =			self.callback_handler.on_evaluate(self.args						,  self.state						,  self.control						,  lowercase_       )
     return metrics






 def 		_snake_case      (  self	: Any						,  lowercase_	: int						,  lowercase_	: List[str]						,  lowercase_	: str=None						,  lowercase_	: str = "test"						,  **lowercase_	: Dict       ):
     snake_case_				:  Dict       =			gen_kwargs.copy()

     snake_case_				:  Dict       =			self.get_test_dataloader(lowercase_       )

     # Temporarily disable metric computation, we will do it in the loop here.
     snake_case_				:  Tuple       =			self.compute_metrics
     snake_case_				:  int       =			None
     snake_case_				:  List[Any]       =			time.time()
     snake_case_				:  int       =			self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
     try:
         snake_case_				:  List[str]       =			eval_loop(
             lowercase_						,  description='''Prediction'''						,  prediction_loss_only=True if compute_metrics is None else None						,  ignore_keys=lowercase_						,  metric_key_prefix=lowercase_						,  )
     finally:
         snake_case_				:  str       =			compute_metrics

     snake_case_				:  int       =			self.args.eval_batch_size * self.args.world_size
     if f"{metric_key_prefix}_jit_compilation_time" in output.metrics:
         start_time += output.metrics[f"{metric_key_prefix}_jit_compilation_time"]
     output.metrics.update(
         speed_metrics(
             lowercase_						,  lowercase_						,  num_samples=output.num_samples						,  num_steps=math.ceil(output.num_samples / total_batch_size       )						,  )       )
     if self.post_process_function is None or self.compute_metrics is None:
         return output

     snake_case_				:  Tuple       =			self.post_process_function(lowercase_						,  lowercase_						,  lowercase_						,  '''predict'''       )
     snake_case_				:  Dict       =			self.compute_metrics(lowercase_       )

     # Prefix all keys with metric_key_prefix + '_'
     for key in list(metrics.keys()       ):
         if not key.startswith(f"{metric_key_prefix}_"       ):
             snake_case_				:  Union[str, Any]       =			metrics.pop(lowercase_       )
     metrics.update(output.metrics       )
     return PredictionOutput(predictions=predictions.predictions						,  label_ids=predictions.label_ids						,  metrics=lowercase_       )





