'''simple docstring'''




from __future__ import annotations

from random import random
from typing import Generic, TypeVar

__lowercase        =    TypeVar('''KT''')
__lowercase        =    TypeVar('''VT''')






class 							a__(   Generic[KT, VT]      ):


			'''simple docstring'''






			def __init__(  self			,       __lowerCAmelCase = "root"			,       __lowerCAmelCase = None):




					"""simple docstring"""


					lowerCAmelCase     =    key
					lowerCAmelCase     =    value
					lowerCAmelCase     =    []



			def __repr__(  self):




					"""simple docstring"""


					return f"Node({self.key}: {self.value})"







			@property
			def 				a_			(  self):




					"""simple docstring"""


					return len(self.forward)







class 							a__(   Generic[KT, VT]      ):


			'''simple docstring'''






			def __init__(  self			,       __lowerCAmelCase = 0.5			,       __lowerCAmelCase = 16):




					"""simple docstring"""


					lowerCAmelCase     =    Node[KT, VT]()
					lowerCAmelCase     =    0
					lowerCAmelCase     =    p
					lowerCAmelCase     =    max_level



			def __str__(  self):




					"""simple docstring"""


					lowerCAmelCase     =    list(self)

					if len(__lowerCAmelCase) == 0:
							return f"SkipList(level={self.level})"

					lowerCAmelCase     =    max((len(str(__lowerCAmelCase)) for item in items)			,       default=4)
					lowerCAmelCase     =    max(__lowerCAmelCase			,       4) + 4

					lowerCAmelCase     =    self.head
					lowerCAmelCase     =    []

					lowerCAmelCase     =    node.forward.copy()
					lines.append(f"[{node.key}]".ljust(__lowerCAmelCase			,       """-""") + """* """ * len(__lowerCAmelCase))
					lines.append(""" """ * label_size + """| """ * len(__lowerCAmelCase))

					while len(node.forward) != 0:
							lowerCAmelCase     =    node.forward[0]

							lines.append(
							    f"[{node.key}]".ljust(__lowerCAmelCase			,       """-""")
							    + """ """.join(str(n.key) if n.key == node.key else """|""" for n in forwards))
							lines.append(""" """ * label_size + """| """ * len(__lowerCAmelCase))
							lowerCAmelCase     =    node.forward

					lines.append("""None""".ljust(__lowerCAmelCase) + """* """ * len(__lowerCAmelCase))
					return f"SkipList(level={self.level})\n" + "\n".join(__lowerCAmelCase)



			def __iter__(  self):




					"""simple docstring"""


					lowerCAmelCase     =    self.head

					while len(node.forward) != 0:
							yield node.forward[0].key
							lowerCAmelCase     =    node.forward[0]



			def 				a_			(  self):




					"""simple docstring"""


					lowerCAmelCase     =    1
					while random() < self.p and level < self.max_level:
							level += 1

					return level



			def 				a_			(  self			,       __lowerCAmelCase):




					"""simple docstring"""


					lowerCAmelCase     =    []

					lowerCAmelCase     =    self.head

					for i in reversed(range(self.level)):
							# i < node.level - When node level is lesser than `i` decrement `i`.
							# node.forward[i].key < key - Jumping to node with key value higher
							#                             or equal to searched key would result
							#                             in skipping searched key.
							while i < node.level and node.forward[i].key < key:
									lowerCAmelCase     =    node.forward[i]
							# Each leftmost node (relative to searched node) will potentially have to
							# be updated.
							update_vector.append(__lowerCAmelCase)

					update_vector.reverse()  # Note that we were inserting values in reverse order.

					# len(node.forward) != 0 - If current node doesn't contain any further
					#                          references then searched key is not present.
					# node.forward[0].key == key - Next node key should be equal to search key
					#                              if key is present.
					if len(node.forward) != 0 and node.forward[0].key == key:
							return node.forward[0], update_vector
					else:
							return None, update_vector



			def 				a_			(  self			,       __lowerCAmelCase):




					"""simple docstring"""


					lowerCAmelCase   ,	lowerCAmelCase     =    self._locate_node(__lowerCAmelCase)

					if node is not None:
							for i, update_node in enumerate(__lowerCAmelCase):
									# Remove or replace all references to removed node.
									if update_node.level > i and update_node.forward[i].key == key:
											if node.level > i:
													lowerCAmelCase     =    node.forward[i]
											else:
													lowerCAmelCase     =    update_node.forward[:i]



			def 				a_			(  self			,       __lowerCAmelCase			,       __lowerCAmelCase):




					"""simple docstring"""


					lowerCAmelCase   ,	lowerCAmelCase     =    self._locate_node(__lowerCAmelCase)
					if node is not None:
							lowerCAmelCase     =    value
					else:
							lowerCAmelCase     =    self.random_level()

							if level > self.level:
									# After level increase we have to add additional nodes to head.
									for _ in range(self.level - 1			,       __lowerCAmelCase):
											update_vector.append(self.head)
									lowerCAmelCase     =    level

							lowerCAmelCase     =    Node(__lowerCAmelCase			,       __lowerCAmelCase)

							for i, update_node in enumerate(update_vector[:level]):
									# Change references to pass through new node.
									if update_node.level > i:
											new_node.forward.append(update_node.forward[i])

									if update_node.level < i + 1:
											update_node.forward.append(__lowerCAmelCase)
									else:
											lowerCAmelCase     =    new_node







			def 				a_			(  self			,       __lowerCAmelCase):




					"""simple docstring"""


					lowerCAmelCase   ,	lowerCAmelCase     =    self._locate_node(__lowerCAmelCase)

					if node is not None:
							return node.value

					return None







def 							snake_case__				(     )       ->      Optional[Any]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()
		skip_list.insert("""Key1""" ,  3					)
		skip_list.insert("""Key2""" ,  12					)
		skip_list.insert("""Key3""" ,  41					)
		skip_list.insert("""Key4""" ,  -19					)

		lowerCAmelCase     =    skip_list.head
		lowerCAmelCase     =    {}
		while node.level != 0:
				lowerCAmelCase     =    node.forward[0]
				lowerCAmelCase     =    node.value

		assert len(lowerCamelCase_					) == 4
		assert all_values["Key1"] == 3
		assert all_values["Key2"] == 12
		assert all_values["Key3"] == 41
		assert all_values["Key4"] == -19






def 							snake_case__				(     )       ->      Tuple:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()
		skip_list.insert("""Key1""" ,  10					)
		skip_list.insert("""Key1""" ,  12					)

		skip_list.insert("""Key5""" ,  7					)
		skip_list.insert("""Key7""" ,  10					)
		skip_list.insert("""Key10""" ,  5					)

		skip_list.insert("""Key7""" ,  7					)
		skip_list.insert("""Key5""" ,  5					)
		skip_list.insert("""Key10""" ,  10					)

		lowerCAmelCase     =    skip_list.head
		lowerCAmelCase     =    {}
		while node.level != 0:
				lowerCAmelCase     =    node.forward[0]
				lowerCAmelCase     =    node.value

		if len(lowerCamelCase_					) != 4:
				print()
		assert len(lowerCamelCase_					) == 4
		assert all_values["Key1"] == 12
		assert all_values["Key7"] == 7
		assert all_values["Key5"] == 5
		assert all_values["Key10"] == 10






def 							snake_case__				(     )       ->      Optional[int]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()
		assert skip_list.find("""Some key"""					) is None






def 							snake_case__				(     )       ->      int:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()

		skip_list.insert("""Key2""" ,  20					)
		assert skip_list.find("""Key2"""					) == 20

		skip_list.insert("""Some Key""" ,  10					)
		skip_list.insert("""Key2""" ,  8					)
		skip_list.insert("""V""" ,  13					)

		assert skip_list.find("""Y"""					) is None
		assert skip_list.find("""Key2"""					) == 8
		assert skip_list.find("""Some Key"""					) == 10
		assert skip_list.find("""V"""					) == 13






def 							snake_case__				(     )       ->      Optional[Any]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()
		skip_list.delete("""Some key"""					)

		assert len(skip_list.head.forward					) == 0






def 							snake_case__				(     )       ->      Optional[Any]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()

		skip_list.insert("""Key1""" ,  12					)
		skip_list.insert("""V""" ,  13					)
		skip_list.insert("""X""" ,  14					)
		skip_list.insert("""Key2""" ,  15					)

		skip_list.delete("""V"""					)
		skip_list.delete("""Key2"""					)

		assert skip_list.find("""V"""					) is None
		assert skip_list.find("""Key2"""					) is None






def 							snake_case__				(     )       ->      List[str]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()

		skip_list.insert("""Key1""" ,  12					)
		skip_list.insert("""V""" ,  13					)
		skip_list.insert("""X""" ,  14					)
		skip_list.insert("""Key2""" ,  15					)

		skip_list.delete("""V"""					)
		assert skip_list.find("""V"""					) is None
		assert skip_list.find("""X"""					) == 14
		assert skip_list.find("""Key1"""					) == 12
		assert skip_list.find("""Key2"""					) == 15

		skip_list.delete("""X"""					)
		assert skip_list.find("""V"""					) is None
		assert skip_list.find("""X"""					) is None
		assert skip_list.find("""Key1"""					) == 12
		assert skip_list.find("""Key2"""					) == 15

		skip_list.delete("""Key1"""					)
		assert skip_list.find("""V"""					) is None
		assert skip_list.find("""X"""					) is None
		assert skip_list.find("""Key1"""					) is None
		assert skip_list.find("""Key2"""					) == 15

		skip_list.delete("""Key2"""					)
		assert skip_list.find("""V"""					) is None
		assert skip_list.find("""X"""					) is None
		assert skip_list.find("""Key1"""					) is None
		assert skip_list.find("""Key2"""					) is None






def 							snake_case__				(     )       ->      str:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()

		skip_list.insert("""Key1""" ,  12					)
		skip_list.insert("""V""" ,  13					)
		skip_list.insert("""X""" ,  142					)
		skip_list.insert("""Key2""" ,  15					)

		skip_list.delete("""X"""					)

		def traverse_keys(_A:   Union[str, Any]					):
				yield node.key
				for forward_node in node.forward:
						yield from traverse_keys(lowerCamelCase_					)

		assert len(set(traverse_keys(skip_list.head					)					)					) == 4






def 							snake_case__				(     )       ->      str:

		'''simple docstring'''


		def is_sorted(_A:   Optional[Any]					):
				return all(next_item >= item for item, next_item in zip(lowerCamelCase_ ,  lst[1:]					)					)

		lowerCAmelCase     =    SkipList()
		for i in range(10					):
				skip_list.insert(lowerCamelCase_ ,  lowerCamelCase_					)
		assert is_sorted(list(lowerCamelCase_					)					)
		skip_list.delete(5					)
		skip_list.delete(8					)
		skip_list.delete(2					)
		assert is_sorted(list(lowerCamelCase_					)					)
		skip_list.insert(-12 ,  -12					)
		skip_list.insert(77 ,  77					)
		assert is_sorted(list(lowerCamelCase_					)					)






def 							snake_case__				(     )       ->      str:

		'''simple docstring'''


		for _ in range(100					):
				# Repeat test 100 times due to the probabilistic nature of skip list
				# random values == random bugs
				test_insert()
				test_insert_overrides_existing_value()

				test_searching_empty_list_returns_none()
				test_search()

				test_deleting_item_from_empty_list_do_nothing()
				test_deleted_items_are_not_founded_by_find_method()
				test_delete_removes_only_given_key()
				test_delete_doesnt_leave_dead_nodes()

				test_iter_always_yields_sorted_values()






def 							snake_case__				(     )       ->      List[Any]:

		'''simple docstring'''


		lowerCAmelCase     =    SkipList()
		skip_list.insert(2 ,  """2"""					)
		skip_list.insert(4 ,  """4"""					)
		skip_list.insert(6 ,  """4"""					)
		skip_list.insert(4 ,  """5"""					)
		skip_list.insert(8 ,  """4"""					)
		skip_list.insert(9 ,  """4"""					)

		skip_list.delete(4					)

		print(lowerCamelCase_					)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()












from jiwer import compute_measures

import datasets


A__      :     Tuple       =					'\\n@inproceedings{inproceedings,\n    author = {Morris, Andrew and Maier, Viktoria and Green, Phil},\n    year = {2004},\n    month = {01},\n    pages = {},\n    title = {From WER and RIL to MER and WIL: improved evaluation measures for connected speech recognition.}\n}\n'

A__      :     Optional[int]       =					'\\nWord error rate (WER) is a common metric of the performance of an automatic speech recognition system.\n\nThe general difficulty of measuring performance lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived from the Levenshtein distance, working at the word level instead of the phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to focus any research effort.\n\nThis problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate.\n\nWord error rate can then be computed as:\n\nWER = (S + D + I) / N = (S + D + I) / (S + D + C)\n\nwhere\n\nS is the number of substitutions,\nD is the number of deletions,\nI is the number of insertions,\nC is the number of correct words,\nN is the number of words in the reference (N=S+D+C).\n\nThis value indicates the average number of errors per reference word. The lower the value, the better the\nperformance of the ASR system with a WER of 0 being a perfect score.\n'

A__      :     Dict       =					'\nCompute WER score of transcribed segments against references.\n\nArgs:\n    references: List of references for each speech input.\n    predictions: List of transcriptions to score.\n    concatenate_texts (bool, default=False): Whether to concatenate all input texts or compute WER iteratively.\n\nReturns:\n    (float): the word error rate\n\nExamples:\n\n    >>> predictions = ["this is the prediction", "there is an other sample"]\n    >>> references = ["this is the reference", "there is another one"]\n    >>> wer = datasets.load_metric("wer")\n    >>> wer_score = wer.compute(predictions=predictions, references=references)\n    >>> print(wer_score)\n    0.5\n'
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION						,_KWARGS_DESCRIPTION      )
class  _UpperCAmelCase   (			datasets.Metric      ):

				"""simple docstring"""




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

								'''simple docstring'''
								return datasets.MetricInfo(
								    description=_DESCRIPTION,    citation=_CITATION,    inputs_description=_KWARGS_DESCRIPTION,    features=datasets.Features(
								        {
								            '''predictions''': datasets.Value('''string''',    id='''sequence'''    ),
								            '''references''': datasets.Value('''string''',    id='''sequence'''    ),
								        }    ),    codebase_urls=['''https://github.com/jitsi/jiwer/'''],    reference_urls=[
								        '''https://en.wikipedia.org/wiki/Word_error_rate''',
								    ],    )




				def 							lowercase__  (	self		:       Union[str, Any],    lowerCamelCase		:       str=None,    lowerCamelCase		:       Union[str, Any]=None,    lowerCamelCase		:       List[str]=False    ):

								'''simple docstring'''
								if concatenate_texts:
												return compute_measures(lowerCamelCase,    lowerCamelCase    )["wer"]
								else:
												lowercase__  					=     0
												lowercase__  					=     0
												for prediction, reference in zip(lowerCamelCase,    lowerCamelCase    ):
																lowercase__  					=     compute_measures(lowerCamelCase,    lowerCamelCase    )
																incorrect += measures["substitutions"] + measures["deletions"] + measures["insertions"]
																total += measures["substitutions"] + measures["deletions"] + measures["hits"]
												return incorrect / total




