






"""simple docstring"""


from __future__ import annotations

from collections.abc import MutableSequence


class 					snake_case		:


   '''simple docstring'''

   def __init__(	self :     Dict,       _lowerCamelCase :     int,       _lowerCamelCase :     MutableSequence[float]  ):

     '''simple docstring'''
     if len(_lowerCamelCase  ) != degree + 1:
       raise ValueError(
           '''The number of coefficients should be equal to the degree + 1.'''  )

     __A									= list(_lowerCamelCase  )
     __A									= degree


   def __add__(	self :     List[Any],       _lowerCamelCase :     Polynomial  ):

     '''simple docstring'''

     if self.degree > polynomial_a.degree:
       __A									= self.coefficients[:]
       for i in range(polynomial_a.degree + 1  ):
         coefficients[i] += polynomial_a.coefficients[i]
       return Polynomial(self.degree,       _lowerCamelCase  )
     else:
       __A									= polynomial_a.coefficients[:]
       for i in range(self.degree + 1  ):
         coefficients[i] += self.coefficients[i]
       return Polynomial(polynomial_a.degree,       _lowerCamelCase  )


   def __sub__(	self :     Optional[int],       _lowerCamelCase :     Polynomial  ):

     '''simple docstring'''
     return self + polynomial_a * Polynomial(0,       [-1]  )


   def __neg__(	self :     Optional[int]  ):

     '''simple docstring'''
     return Polynomial(self.degree,       [-c for c in self.coefficients]  )


   def __mul__(	self :     List[Any],       _lowerCamelCase :     Polynomial  ):

     '''simple docstring'''
     __A									= [0] * (self.degree + polynomial_a.degree + 1)
     for i in range(self.degree + 1  ):
       for j in range(polynomial_a.degree + 1  ):
         coefficients[i + j] += (
             self.coefficients[i] * polynomial_a.coefficients[j]
         )

     return Polynomial(self.degree + polynomial_a.degree,       _lowerCamelCase  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     Union[str, Any],       _lowerCamelCase :     int | float  ):

     '''simple docstring'''
     __A									= 0
     for i in range(self.degree + 1  ):
       result += self.coefficients[i] * (substitution**i)
     return result


   def __str__(	self :     Tuple  ):

     '''simple docstring'''
     __A									= ''''''
     for i in range(self.degree,       -1,       -1  ):
       if self.coefficients[i] == 0:
         continue
       elif self.coefficients[i] > 0:
         if polynomial:
           polynomial += " + "
       else:
         polynomial += " - "

       if i == 0:
         polynomial += str(abs(self.coefficients[i]  )  )
       elif i == 1:
         polynomial += str(abs(self.coefficients[i]  )  ) + "x"
       else:
         polynomial += str(abs(self.coefficients[i]  )  ) + "x^" + str(_lowerCamelCase  )

     return polynomial


   def __repr__(	self :     List[str]  ):

     '''simple docstring'''
     return self.__str__()


   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[int]  ):

     '''simple docstring'''
     __A									= [0] * self.degree
     for i in range(self.degree  ):
       __A									= self.coefficients[i + 1] * (i + 1)
     return Polynomial(self.degree - 1,       _lowerCamelCase  )


   def 				_SCREAMING_SNAKE_CASE				(	self :     List[str],       _lowerCamelCase :     int | float = 0  ):

     '''simple docstring'''
     __A									= [0] * (self.degree + 2)
     __A									= constant
     for i in range(self.degree + 1  ):
       __A									= self.coefficients[i] / (i + 1)
     return Polynomial(self.degree + 1,       _lowerCamelCase  )


   def __eq__(	self :     Optional[int],       _lowerCamelCase :     object  ):

     '''simple docstring'''
     if not isinstance(_lowerCamelCase,       _lowerCamelCase  ):
       return False

     if self.degree != polynomial_a.degree:
       return False

     for i in range(self.degree + 1  ):
       if self.coefficients[i] != polynomial_a.coefficients[i]:
         return False

     return True






   def __ne__(	self :     List[Any],       _lowerCamelCase :     object  ):

     '''simple docstring'''
     return not self.__eq__(_lowerCamelCase  )












"""simple docstring"""


from typing import Dict, List

from nltk.translate import gleu_score

import datasets
from datasets import MetricInfo


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

lowercase_				     =     '\\nThe BLEU score has some undesirable properties when used for single\nsentences, as it was designed to be a corpus measure. We therefore\nuse a slightly different score for our RL experiments which we call\nthe \'GLEU score\'. For the GLEU score, we record all sub-sequences of\n1, 2, 3 or 4 tokens in output and target sequence (n-grams). We then\ncompute a recall, which is the ratio of the number of matching n-grams\nto the number of total n-grams in the target (ground truth) sequence,\nand a precision, which is the ratio of the number of matching n-grams\nto the number of total n-grams in the generated output sequence. Then\nGLEU score is simply the minimum of recall and precision. This GLEU\nscore\'s range is always between 0 (no matches) and 1 (all match) and\nit is symmetrical when switching output and target. According to\nour experiments, GLEU score correlates quite well with the BLEU\nmetric on a corpus level but does not have its drawbacks for our per\nsentence reward objective.\n'

lowercase_				     =     '\\nComputes corpus-level Google BLEU (GLEU) score of translated segments against one or more references.\nInstead of averaging the sentence level GLEU scores (i.e. macro-average precision), Wu et al. (2016) sum up the matching\ntokens and the max of hypothesis and reference tokens for each sentence, then compute using the aggregate values.\n\nArgs:\n    predictions (list of str): list of translations to score.\n        Each translation should be tokenized into a list of tokens.\n    references (list of list of str): list of lists of references for each translation.\n        Each reference should be tokenized into a list of tokens.\n    min_len (int): The minimum order of n-gram this function should extract. Defaults to 1.\n    max_len (int): The maximum order of n-gram this function should extract. Defaults to 4.\n\nReturns:\n    \'google_bleu\': google_bleu score\n\nExamples:\n    Example 1:\n        >>> hyp1 = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'which\',\n        ...         \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'always\',\n        ...         \'disobeys\', \'the\', \'commands\', \'of\', \'the\', \'cat\']\n        >>> ref1a = [\'It\', \'is\', \'the\', \'guiding\', \'principle\', \'which\',\n        ...          \'guarantees\', \'the\', \'rubber\', \'duck\', \'forces\', \'never\',\n        ...          \'being\', \'under\', \'the\', \'command\', \'of\', \'the\', \'cat\']\n\n        >>> hyp2 = [\'he\', \'read\', \'the\', \'book\', \'because\', \'he\', \'was\',\n        ...         \'interested\', \'in\', \'world\', \'history\']\n        >>> ref2a = [\'he\', \'was\', \'interested\', \'in\', \'world\', \'history\',\n        ...          \'because\', \'he\', \'read\', \'the\', \'book\']\n\n        >>> list_of_references = [[ref1a], [ref2a]]\n        >>> hypotheses = [hyp1, hyp2]\n        >>> google_bleu = datasets.load_metric("google_bleu")\n        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references)\n        >>> print(round(results["google_bleu"], 2))\n        0.44\n\n    Example 2:\n        >>> hyp1 = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'which\',\n        ...         \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'always\',\n        ...         \'disobeys\', \'the\', \'commands\', \'of\', \'the\', \'cat\']\n        >>> ref1a = [\'It\', \'is\', \'the\', \'guiding\', \'principle\', \'which\',\n        ...          \'guarantees\', \'the\', \'rubber\', \'duck\', \'forces\', \'never\',\n        ...          \'being\', \'under\', \'the\', \'command\', \'of\', \'the\', \'cat\']\n        >>> ref1b = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'that\',\n        ...          \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'will\', \'never\',\n        ...          \'heed\', \'the\', \'cat\', \'commands\']\n        >>> ref1c = [\'It\', \'is\', \'the\', \'practical\', \'guide\', \'for\', \'the\',\n        ...          \'rubber\', \'duck\', \'army\', \'never\', \'to\', \'heed\', \'the\', \'directions\',\n        ...          \'of\', \'the\', \'cat\']\n\n        >>> hyp2 = [\'he\', \'read\', \'the\', \'book\', \'because\', \'he\', \'was\',\n        ...         \'interested\', \'in\', \'world\', \'history\']\n        >>> ref2a = [\'he\', \'was\', \'interested\', \'in\', \'world\', \'history\',\n        ...          \'because\', \'he\', \'read\', \'the\', \'book\']\n\n        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]\n        >>> hypotheses = [hyp1, hyp2]\n        >>> google_bleu = datasets.load_metric("google_bleu")\n        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references)\n        >>> print(round(results["google_bleu"], 2))\n        0.61\n\n    Example 3:\n        >>> hyp1 = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'which\',\n        ...         \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'always\',\n        ...         \'disobeys\', \'the\', \'commands\', \'of\', \'the\', \'cat\']\n        >>> ref1a = [\'It\', \'is\', \'the\', \'guiding\', \'principle\', \'which\',\n        ...          \'guarantees\', \'the\', \'rubber\', \'duck\', \'forces\', \'never\',\n        ...          \'being\', \'under\', \'the\', \'command\', \'of\', \'the\', \'cat\']\n        >>> ref1b = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'that\',\n        ...          \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'will\', \'never\',\n        ...          \'heed\', \'the\', \'cat\', \'commands\']\n        >>> ref1c = [\'It\', \'is\', \'the\', \'practical\', \'guide\', \'for\', \'the\',\n        ...          \'rubber\', \'duck\', \'army\', \'never\', \'to\', \'heed\', \'the\', \'directions\',\n        ...          \'of\', \'the\', \'cat\']\n\n        >>> hyp2 = [\'he\', \'read\', \'the\', \'book\', \'because\', \'he\', \'was\',\n        ...         \'interested\', \'in\', \'world\', \'history\']\n        >>> ref2a = [\'he\', \'was\', \'interested\', \'in\', \'world\', \'history\',\n        ...          \'because\', \'he\', \'read\', \'the\', \'book\']\n\n        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]\n        >>> hypotheses = [hyp1, hyp2]\n        >>> google_bleu = datasets.load_metric("google_bleu")\n        >>> results = google_bleu.compute(predictions=hypotheses, references=list_of_references, min_len=2)\n        >>> print(round(results["google_bleu"], 2))\n        0.53\n\n    Example 4:\n        >>> hyp1 = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'which\',\n        ...         \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'always\',\n        ...         \'disobeys\', \'the\', \'commands\', \'of\', \'the\', \'cat\']\n        >>> ref1a = [\'It\', \'is\', \'the\', \'guiding\', \'principle\', \'which\',\n        ...          \'guarantees\', \'the\', \'rubber\', \'duck\', \'forces\', \'never\',\n        ...          \'being\', \'under\', \'the\', \'command\', \'of\', \'the\', \'cat\']\n        >>> ref1b = [\'It\', \'is\', \'a\', \'guide\', \'to\', \'action\', \'that\',\n        ...          \'ensures\', \'that\', \'the\', \'rubber\', \'duck\', \'will\', \'never\',\n        ...          \'heed\', \'the\', \'cat\', \'commands\']\n        >>> ref1c = [\'It\', \'is\', \'the\', \'practical\', \'guide\', \'for\', \'the\',\n        ...          \'rubber\', \'duck\', \'army\', \'never\', \'to\', \'heed\', \'the\', \'directions\',\n        ...          \'of\', \'the\', \'cat\']\n\n        >>> hyp2 = [\'he\', \'read\', \'the\', \'book\', \'because\', \'he\', \'was\',\n        ...         \'interested\', \'in\', \'world\', \'history\']\n        >>> ref2a = [\'he\', \'was\', \'interested\', \'in\', \'world\', \'history\',\n        ...          \'because\', \'he\', \'read\', \'the\', \'book\']\n\n        >>> list_of_references = [[ref1a, ref1b, ref1c], [ref2a]]\n        >>> hypotheses = [hyp1, hyp2]\n        >>> google_bleu = datasets.load_metric("google_bleu")\n        >>> results = google_bleu.compute(predictions=hypotheses,references=list_of_references, min_len=2, max_len=6)\n        >>> print(round(results["google_bleu"], 2))\n        0.4\n'


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


   '''simple docstring'''

   def 				_SCREAMING_SNAKE_CASE				(	self :     Union[str, Any]  ):

     '''simple docstring'''
     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 				_SCREAMING_SNAKE_CASE				(	self :     str,       _lowerCamelCase :     List[List[List[str]]],       _lowerCamelCase :     List[List[str]],       _lowerCamelCase :     int = 1,       _lowerCamelCase :     int = 4,       ):

     '''simple docstring'''
     return {
         "google_bleu": gleu_score.corpus_gleu(
             list_of_references=_lowerCamelCase,       hypotheses=_lowerCamelCase,       min_len=_lowerCamelCase,       max_len=_lowerCamelCase  )
     }




