


"""simple docstring"""
from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

UpperCAmelCase				=						TypeVar("""T""")

def 				_snake_case      (   __snake_case							:      int   ):




   """simple docstring"""







   return (position - 1) // 2

def 				_snake_case      (   __snake_case							:      int   ):




   """simple docstring"""







   return (2 * position) + 1

def 				_snake_case      (   __snake_case							:      int   ):




   """simple docstring"""







   return (2 * position) + 2




class 	lowercase__				(					Generic[T]				):





   def __init__(							self)  ->  None:
      _lowerCamelCase	:					list[tuple[T, int]]   =		[]
      _lowerCamelCase	:					dict[T, int]   =		{}
      _lowerCamelCase	:					int   =		0





   def __len__(							self)  ->  int:
      return self.elements





   def __repr__(							self)  ->  str:
      return str(self.heap)





   def 		UpperCamelCase_  (							self)  ->  bool:
      # Check if the priority queue is empty
      return self.elements == 0





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Add an element with given priority to the queue
      self.heap.append((elem, weight))
      _lowerCamelCase	:					Any   =		self.elements
      self.elements += 1
      self._bubble_up(SCREAMING_SNAKE_CASE)





   def 		UpperCamelCase_  (							self)  ->  T:
      # Remove and return the element with lowest weight (highest priority)
      if self.elements > 1:
         self._swap_nodes(0      ,   self.elements - 1)
      _lowerCamelCase   ,    _lowerCamelCase	:					Dict   =		self.heap.pop()
      del self.position_map[elem]
      self.elements -= 1
      if self.elements > 0:
         _lowerCamelCase   ,    _lowerCamelCase	:					Tuple   =		self.heap[0]
         self._bubble_down(SCREAMING_SNAKE_CASE)
      return elem





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Update the weight of the given key
      _lowerCamelCase	:					List[Any]   =		self.position_map[elem]
      _lowerCamelCase	:					Tuple   =		(elem, weight)
      if position > 0:
         _lowerCamelCase	:					List[str]   =		get_parent_position(SCREAMING_SNAKE_CASE)
         _lowerCamelCase   ,    _lowerCamelCase	:					int   =		self.heap[parent_position]
         if parent_weight > weight:
            self._bubble_up(SCREAMING_SNAKE_CASE)
         else:
            self._bubble_down(SCREAMING_SNAKE_CASE)
      else:
         self._bubble_down(SCREAMING_SNAKE_CASE)





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Place a node at the proper position (upward movement) [to be used internally
      # only]
      _lowerCamelCase	:					int   =		self.position_map[elem]
      if curr_pos == 0:
         return None
      _lowerCamelCase	:					List[Any]   =		get_parent_position(SCREAMING_SNAKE_CASE)
      _lowerCamelCase   ,    _lowerCamelCase	:					Dict   =		self.heap[curr_pos]
      _lowerCamelCase   ,    _lowerCamelCase	:					List[Any]   =		self.heap[parent_position]
      if parent_weight > weight:
         self._swap_nodes(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)
         return self._bubble_up(SCREAMING_SNAKE_CASE)
      return None





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Place a node at the proper position (downward movement) [to be used
      # internally only]
      _lowerCamelCase	:					int   =		self.position_map[elem]
      _lowerCamelCase   ,    _lowerCamelCase	:					Dict   =		self.heap[curr_pos]
      _lowerCamelCase	:					str   =		get_child_left_position(SCREAMING_SNAKE_CASE)
      _lowerCamelCase	:					int   =		get_child_right_position(SCREAMING_SNAKE_CASE)
      if child_left_position < self.elements and child_right_position < self.elements:
         _lowerCamelCase   ,    _lowerCamelCase	:					Optional[Any]   =		self.heap[child_left_position]
         _lowerCamelCase   ,    _lowerCamelCase	:					Dict   =		self.heap[child_right_position]
         if child_right_weight < child_left_weight and child_right_weight < weight:
            self._swap_nodes(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)
            return self._bubble_down(SCREAMING_SNAKE_CASE)
      if child_left_position < self.elements:
         _lowerCamelCase   ,    _lowerCamelCase	:					Dict   =		self.heap[child_left_position]
         if child_left_weight < weight:
            self._swap_nodes(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)
            return self._bubble_down(SCREAMING_SNAKE_CASE)
      else:
         return None
      if child_right_position < self.elements:
         _lowerCamelCase   ,    _lowerCamelCase	:					int   =		self.heap[child_right_position]
         if child_right_weight < weight:
            self._swap_nodes(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)
            return self._bubble_down(SCREAMING_SNAKE_CASE)
      return None





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Swap the nodes at the given positions
      _lowerCamelCase	:					List[str]   =		self.heap[nodea_pos][0]
      _lowerCamelCase	:					Dict   =		self.heap[nodea_pos][0]
      _lowerCamelCase   ,    _lowerCamelCase	:					List[Any]   =		(
          self.heap[nodea_pos],
          self.heap[nodea_pos],
      )
      _lowerCamelCase	:					Optional[Any]   =		nodea_pos
      _lowerCamelCase	:					int   =		nodea_pos







class 	lowercase__				(					Generic[T]				):





   def __init__(							self)  ->  None:
      _lowerCamelCase	:					dict[T, dict[T, int]]   =		{}
      _lowerCamelCase	:					int   =		0





   def __repr__(							self)  ->  str:
      return str(self.connections)





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





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Add a node in the graph if it is not in the graph
      if node not in self.connections:
         _lowerCamelCase	:					int   =		{}
         self.nodes += 1





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE)  ->  None:
      # Add an edge between 2 nodes in the graph
      self.add_node(SCREAMING_SNAKE_CASE)
      self.add_node(SCREAMING_SNAKE_CASE)
      _lowerCamelCase	:					List[Any]   =		weight
      _lowerCamelCase	:					int   =		weight







def 				_snake_case      (   __snake_case							:      GraphUndirectedWeighted[T]						, ):




   """simple docstring"""







   _lowerCamelCase	:					dict[T, int]   =		{node: maxsize for node in graph.connections}
   _lowerCamelCase	:					dict[T, T | None]   =		{node: None for node in graph.connections}

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

   if priority_queue.is_empty():
      return dist, parent

   # initialization
   _lowerCamelCase	:					List[str]   =		priority_queue.extract_min()
   _lowerCamelCase	:					str   =		0
   for neighbour in graph.connections[node]:
      if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
         _lowerCamelCase	:					List[Any]   =		dist[node] + graph.connections[node][neighbour]
         priority_queue.update_key(__snake_case						, dist[neighbour]   )
         _lowerCamelCase	:					Tuple   =		node

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





"""simple docstring"""
from typing import Dict, List

from nltk.translate import gleu_score

import datasets
from datasets import MetricInfo


UpperCAmelCase				=						"""\
@misc{wu2016googles,
      title={Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation},
      author={Yonghui Wu and Mike Schuster and Zhifeng Chen and Quoc V. Le and Mohammad Norouzi and Wolfgang Macherey
              and Maxim Krikun and Yuan Cao and Qin Gao and Klaus Macherey and Jeff Klingner and Apurva Shah and Melvin
              Johnson and Xiaobing Liu and Łukasz Kaiser and Stephan Gouws and Yoshikiyo Kato and Taku Kudo and Hideto
              Kazawa and Keith Stevens and George Kurian and Nishant Patil and Wei Wang and Cliff Young and
              Jason Smith and Jason Riesa and Alex Rudnick and Oriol Vinyals and Greg Corrado and Macduff Hughes
              and Jeffrey Dean},
      year={2016},
      eprint={1609.08144},
      archivePrefix={arXiv},
      primaryClass={cs.CL}
}
"""

UpperCAmelCase				=						"""\
The BLEU score has some undesirable properties when used for single
sentences, as it was designed to be a corpus measure. We therefore
use a slightly different score for our RL experiments which we call
the 'GLEU score'. For the GLEU score, we record all sub-sequences of
1, 2, 3 or 4 tokens in output and target sequence (n-grams). We then
compute a recall, which is the ratio of the number of matching n-grams
to the number of total n-grams in the target (ground truth) sequence,
and a precision, which is the ratio of the number of matching n-grams
to the number of total n-grams in the generated output sequence. Then
GLEU score is simply the minimum of recall and precision. This GLEU
score's range is always between 0 (no matches) and 1 (all match) and
it is symmetrical when switching output and target. According to
our experiments, GLEU score correlates quite well with the BLEU
metric on a corpus level but does not have its drawbacks for our per
sentence reward objective.
"""

UpperCAmelCase				=						"""\
Computes corpus-level Google BLEU (GLEU) score of translated segments against one or more references.
Instead of averaging the sentence level GLEU scores (i.e. macro-average precision), Wu et al. (2016) sum up the matching
tokens and the max of hypothesis and reference tokens for each sentence, then compute using the aggregate values.

Args:
    predictions (list of str): list of translations to score.
        Each translation should be tokenized into a list of tokens.
    references (list of list of str): list of lists of references for each translation.
        Each reference should be tokenized into a list of tokens.
    min_len (int): The minimum order of n-gram this function should extract. Defaults to 1.
    max_len (int): The maximum order of n-gram this function should extract. Defaults to 4.

Returns:
    'google_bleu': google_bleu score

Examples:
    Example 1:
        >>> hyp1 = ['It', 'is', 'a', 'guide', 'to', 'action', 'which',
        ...         'ensures', 'that', 'the', 'rubber', 'duck', 'always',
        ...         'disobeys', 'the', 'commands', 'of', 'the', 'cat']
        >>> ref1a = ['It', 'is', 'the', 'guiding', 'principle', 'which',
        ...          'guarantees', 'the', 'rubber', 'duck', 'forces', 'never',
        ...          'being', 'under', 'the', 'command', 'of', 'the', 'cat']

        >>> hyp2 = ['he', 'read', 'the', 'book', 'because', 'he', 'was',
        ...         'interested', 'in', 'world', 'history']
        >>> ref2a = ['he', 'was', 'interested', 'in', 'world', 'history',
        ...          'because', 'he', 'read', 'the', 'book']

        >>> list_of_references = [[ref1a], [ref2a]]
        >>> hypotheses = [hyp1, hyp2]
        >>> google_bleu = datasets.load_metric(\"google_bleu\")
        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references)
        >>> print(round(results[\"google_bleu\"], 2))
        0.44

    Example 2:
        >>> hyp1 = ['It', 'is', 'a', 'guide', 'to', 'action', 'which',
        ...         'ensures', 'that', 'the', 'rubber', 'duck', 'always',
        ...         'disobeys', 'the', 'commands', 'of', 'the', 'cat']
        >>> ref1a = ['It', 'is', 'the', 'guiding', 'principle', 'which',
        ...          'guarantees', 'the', 'rubber', 'duck', 'forces', 'never',
        ...          'being', 'under', 'the', 'command', 'of', 'the', 'cat']
        >>> ref1b = ['It', 'is', 'a', 'guide', 'to', 'action', 'that',
        ...          'ensures', 'that', 'the', 'rubber', 'duck', 'will', 'never',
        ...          'heed', 'the', 'cat', 'commands']
        >>> ref1c = ['It', 'is', 'the', 'practical', 'guide', 'for', 'the',
        ...          'rubber', 'duck', 'army', 'never', 'to', 'heed', 'the', 'directions',
        ...          'of', 'the', 'cat']

        >>> hyp2 = ['he', 'read', 'the', 'book', 'because', 'he', 'was',
        ...         'interested', 'in', 'world', 'history']
        >>> ref2a = ['he', 'was', 'interested', 'in', 'world', 'history',
        ...          'because', 'he', 'read', 'the', 'book']

        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]
        >>> hypotheses = [hyp1, hyp2]
        >>> google_bleu = datasets.load_metric(\"google_bleu\")
        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references)
        >>> print(round(results[\"google_bleu\"], 2))
        0.61

    Example 3:
        >>> hyp1 = ['It', 'is', 'a', 'guide', 'to', 'action', 'which',
        ...         'ensures', 'that', 'the', 'rubber', 'duck', 'always',
        ...         'disobeys', 'the', 'commands', 'of', 'the', 'cat']
        >>> ref1a = ['It', 'is', 'the', 'guiding', 'principle', 'which',
        ...          'guarantees', 'the', 'rubber', 'duck', 'forces', 'never',
        ...          'being', 'under', 'the', 'command', 'of', 'the', 'cat']
        >>> ref1b = ['It', 'is', 'a', 'guide', 'to', 'action', 'that',
        ...          'ensures', 'that', 'the', 'rubber', 'duck', 'will', 'never',
        ...          'heed', 'the', 'cat', 'commands']
        >>> ref1c = ['It', 'is', 'the', 'practical', 'guide', 'for', 'the',
        ...          'rubber', 'duck', 'army', 'never', 'to', 'heed', 'the', 'directions',
        ...          'of', 'the', 'cat']

        >>> hyp2 = ['he', 'read', 'the', 'book', 'because', 'he', 'was',
        ...         'interested', 'in', 'world', 'history']
        >>> ref2a = ['he', 'was', 'interested', 'in', 'world', 'history',
        ...          'because', 'he', 'read', 'the', 'book']

        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]
        >>> hypotheses = [hyp1, hyp2]
        >>> google_bleu = datasets.load_metric(\"google_bleu\")
        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references, min_len=2)
        >>> print(round(results[\"google_bleu\"], 2))
        0.53

    Example 4:
        >>> hyp1 = ['It', 'is', 'a', 'guide', 'to', 'action', 'which',
        ...         'ensures', 'that', 'the', 'rubber', 'duck', 'always',
        ...         'disobeys', 'the', 'commands', 'of', 'the', 'cat']
        >>> ref1a = ['It', 'is', 'the', 'guiding', 'principle', 'which',
        ...          'guarantees', 'the', 'rubber', 'duck', 'forces', 'never',
        ...          'being', 'under', 'the', 'command', 'of', 'the', 'cat']
        >>> ref1b = ['It', 'is', 'a', 'guide', 'to', 'action', 'that',
        ...          'ensures', 'that', 'the', 'rubber', 'duck', 'will', 'never',
        ...          'heed', 'the', 'cat', 'commands']
        >>> ref1c = ['It', 'is', 'the', 'practical', 'guide', 'for', 'the',
        ...          'rubber', 'duck', 'army', 'never', 'to', 'heed', 'the', 'directions',
        ...          'of', 'the', 'cat']

        >>> hyp2 = ['he', 'read', 'the', 'book', 'because', 'he', 'was',
        ...         'interested', 'in', 'world', 'history']
        >>> ref2a = ['he', 'was', 'interested', 'in', 'world', 'history',
        ...          'because', 'he', 'read', 'the', 'book']

        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]
        >>> hypotheses = [hyp1, hyp2]
        >>> google_bleu = datasets.load_metric(\"google_bleu\")
        >>> results = google_bleu.compute(predictions=hypotheses,references=list_of_references, min_len=2, max_len=6)
        >>> print(round(results[\"google_bleu\"], 2))
        0.4
"""




@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION ,_KWARGS_DESCRIPTION				)
class 	lowercase__				(					datasets.Metric				):





   def 		UpperCamelCase_  (							self)  ->  MetricInfo:
      return datasets.MetricInfo(
          description=_DESCRIPTION      ,   citation=_CITATION      ,   inputs_description=_KWARGS_DESCRIPTION      ,   features=datasets.Features(
              {
                  """predictions""": datasets.Sequence(datasets.Value("""string"""      ,   id="""token""")      ,   id="""sequence"""),
                  """references""": datasets.Sequence(
                      datasets.Sequence(datasets.Value("""string"""      ,   id="""token""")      ,   id="""sequence""")      ,   id="""references"""),
              })      ,   )





   def 		UpperCamelCase_  (							self      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE = 1      ,   SCREAMING_SNAKE_CASE = 4      ,   )  ->  Dict[str, float]:
      return {
          "google_bleu": gleu_score.corpus_gleu(
              list_of_references=SCREAMING_SNAKE_CASE      ,   hypotheses=SCREAMING_SNAKE_CASE      ,   min_len=SCREAMING_SNAKE_CASE      ,   max_len=SCREAMING_SNAKE_CASE)
      }

