





"""simple docstring"""





def 				lowerCAmelCase_			(      SCREAMING_SNAKE_CASE       :							List[Any]   ):


							'''simple docstring'''







							if not head:
														return True
							# split the list to two parts
							__lowerCamelCase      :      Tuple         =head.next, head
							while fast and fast.next:
														__lowerCamelCase      :      Optional[int]         =fast.next.next
														__lowerCamelCase      :      Tuple         =slow.next
							__lowerCamelCase      :      Optional[Any]         =slow.next
							__lowerCamelCase      :      Dict         =None  # Don't forget here! But forget still works!
							# reverse the second part
							__lowerCamelCase      :      int         =None
							while second:
														__lowerCamelCase      :      List[Any]         =second.next
														__lowerCamelCase      :      Union[str, Any]         =node
														__lowerCamelCase      :      Optional[Any]         =second
														__lowerCamelCase      :      str         =nxt
							# compare two parts
							# second part has the same or one less node
							while node:
														if node.val != head.val:
																					return False
														__lowerCamelCase      :      Union[str, Any]         =node.next
														__lowerCamelCase      :      int         =head.next
							return True






def 				lowerCAmelCase_			(      SCREAMING_SNAKE_CASE       :							Optional[int]   ):


							'''simple docstring'''







							if not head or not head.next:
														return True

							# 1. Get the midpoint (slow)
							__lowerCamelCase      :      str         =head
							while fast and fast.next:
														__lowerCamelCase      :      Dict         =fast.next.next, slow.next

							# 2. Push the second half into the stack
							__lowerCamelCase      :      Optional[Any]         =[slow.val]
							while slow.next:
														__lowerCamelCase      :      List[str]         =slow.next
														stack.append(slow.val   )

							# 3. Comparison
							while stack:
														if stack.pop() != cur.val:
																					return False
														__lowerCamelCase      :      Optional[Any]         =cur.next

							return True






def 				lowerCAmelCase_			(      SCREAMING_SNAKE_CASE       :							List[str]   ):


							'''simple docstring'''







							if not head or not head.next:
														return True
							__lowerCamelCase      :      List[Any]         ={}
							__lowerCamelCase      :      int         =0
							while head:
														if head.val in d:
																					d[head.val].append(SCREAMING_SNAKE_CASE   )
														else:
																					__lowerCamelCase      :      Union[str, Any]         =[pos]
														__lowerCamelCase      :      str         =head.next
														pos += 1
							__lowerCamelCase      :      Any         =pos - 1
							__lowerCamelCase      :      int         =0
							for v in d.values():
														if len(SCREAMING_SNAKE_CASE   ) % 2 != 0:
																					middle += 1
														else:
																					__lowerCamelCase      :      str         =0
																					for i in range(0    ,						len(SCREAMING_SNAKE_CASE   )   ):
																												if v[i] + v[len(SCREAMING_SNAKE_CASE   ) - 1 - step] != checksum:
																																			return False
																												step += 1
														if middle > 1:
																					return False
							return True











"""simple docstring"""





from typing import Dict, List

from nltk.translate import gleu_score

import datasets
from datasets import MetricInfo


_UpperCamelCase							=      '\\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'

_UpperCamelCase							=      '\\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'

_UpperCamelCase							=      '\\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 		SCREAMING_SNAKE_CASE_							(    datasets.Metric   ):
				"""simple docstring"""




				def 					__lowercase  (     self  :Optional[Any]			):
											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 					__lowercase  (     self  :Optional[Any]						,    __lowercase  :List[List[List[str]]]						,    __lowercase  :List[List[str]]						,    __lowercase  :int = 1						,    __lowercase  :int = 4						,    ):
											return {
											    "google_bleu": gleu_score.corpus_gleu(
											        list_of_references=__lowercase						,    hypotheses=__lowercase						,    min_len=__lowercase						,    max_len=__lowercase			)
											}




