



from __future__ import annotations





def   __snake_case			(    _UpperCAmelCase     ,				_UpperCAmelCase     ,				_UpperCAmelCase     ,				_UpperCAmelCase     ,				_UpperCAmelCase     ,				):
    __a		 =       len(_UpperCAmelCase       )

    # If row is equal to the size of the board it means there are a queen in each row in
    # the current board (possible_board)
    if row == n:
        # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
        # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
        boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]       )
        return

    # We iterate each column in the row to find all possible results in each row
    for col in range(_UpperCAmelCase       ):
        # We apply that we learned previously. First we check that in the current board
        # (possible_board) there are not other same value because if there is it means
        # that there are a collision in vertical. Then we apply the two formulas we
        # learned before:
        #
        # 45º: y - x = b or 45: row - col = b
        # 135º: y + x = b or row + col = b.
        #
        # And we verify if the results of this two formulas not exist in their variables
        # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
        #
        # If any or these are True it means there is a collision so we continue to the
        # next value in the for loop.
        if (
            col in possible_board
            or row - col in diagonal_right_collisions
            or row + col in diagonal_left_collisions
        ):
            continue

        # If it is False we call dfs function again and we update the inputs
        depth_first_search(
            [*possible_board, col]     ,				[*diagonal_right_collisions, row - col]     ,				[*diagonal_left_collisions, row + col]     ,				_UpperCAmelCase     ,				_UpperCAmelCase     ,				)





def   __snake_case			(    _UpperCAmelCase       ):
    __a		 =       []
    depth_first_search([]     ,				[]     ,				[]     ,				_UpperCAmelCase     ,				_UpperCAmelCase       )

    # Print all the boards
    for board in boards:
        for column in board:
            print(_UpperCAmelCase       )
        print(''''''       )

    print(len(_UpperCAmelCase       )     ,				'''solutions were found.'''       )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 n_queens_solution(4)










from typing import List

import jiwer
import jiwer.transforms as tr
from packaging import version

import datasets
from datasets.config import PY_VERSION


if PY_VERSION < version.parse('''3.8'''):
 import importlib_metadata
else:
 import importlib.metadata as importlib_metadata


__snake_case		:int   	=  ''''''


if version.parse(importlib_metadata.version('''jiwer''')) < version.parse('''2.3.0'''):

 class 					_A (			tr.AbstractTransform					):



        def __init__(	self							:  List[Any]  ,	__SCREAMING_SNAKE_CASE							:  str = " "):


            '''simple docstring'''

            __a		 =       sentence_delimiter



        def 	_lowerCamelCase    (	self							:  Dict  ,	__SCREAMING_SNAKE_CASE							:  str):


            '''simple docstring'''

            return list(__SCREAMING_SNAKE_CASE)





        def 	_lowerCamelCase    (	self							:  int  ,	__SCREAMING_SNAKE_CASE							:  List[str]):


            '''simple docstring'''

            __a		 =       []
            for sent_idx, sentence in enumerate(__SCREAMING_SNAKE_CASE):
                chars.extend(self.process_string(__SCREAMING_SNAKE_CASE))
                if self.sentence_delimiter is not None and self.sentence_delimiter != "" and sent_idx < len(__SCREAMING_SNAKE_CASE) - 1:
                    chars.append(self.sentence_delimiter)
            return chars


 __snake_case		:Any   	=  tr.Compose(
     [tr.RemoveMultipleSpaces(), tr.Strip(), SentencesToListOfCharacters(SENTENCE_DELIMITER)]
 )
else:
 __snake_case		:Optional[int]   	=  tr.Compose(
     [
         tr.RemoveMultipleSpaces(),
         tr.Strip(),
         tr.ReduceToSingleSentence(SENTENCE_DELIMITER),
         tr.ReduceToListOfListOfChars(),
     ]
 )


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

__snake_case		:Tuple   	=  '''\
Character error rate (CER) is a common metric of the performance of an automatic speech recognition system.

CER is similar to Word Error Rate (WER), but operates on character instead of word. Please refer to docs of WER for further information.

Character error rate can be computed as:

CER = (S + D + I) / N = (S + D + I) / (S + D + C)

where

S is the number of substitutions,
D is the number of deletions,
I is the number of insertions,
C is the number of correct characters,
N is the number of characters in the reference (N=S+D+C).

CER\'s output is not always a number between 0 and 1, in particular when there is a high number of insertions. This value is often associated to the percentage of characters that were incorrectly predicted. The lower the value, the better the
performance of the ASR system with a CER of 0 being a perfect score.
'''

__snake_case		:Tuple   	=  '''
Computes CER score of transcribed segments against references.
Args:
    references: list of references for each speech input.
    predictions: list of transcribtions to score.
    concatenate_texts: Whether or not to concatenate sentences before evaluation, set to True for more accurate result.
Returns:
    (float): the character error rate

Examples:

    >>> predictions = ["this is the prediction", "there is an other sample"]
    >>> references = ["this is the reference", "there is another one"]
    >>> cer = datasets.load_metric("cer")
    >>> cer_score = cer.compute(predictions=predictions, references=references)
    >>> print(cer_score)
    0.34146341463414637
'''

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



       def 	_lowerCamelCase    (	self							:  Optional[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''',
                   '''https://sites.google.com/site/textdigitisation/qualitymeasures/computingerrorrates''',
               ]  ,	)





       def 	_lowerCamelCase    (	self							:  Optional[int]  ,	__SCREAMING_SNAKE_CASE							:  str  ,	__SCREAMING_SNAKE_CASE							:  List[Any]  ,	__SCREAMING_SNAKE_CASE							:  Dict=False):


           '''simple docstring'''

           if concatenate_texts:
               return jiwer.compute_measures(
                   __SCREAMING_SNAKE_CASE  ,	__SCREAMING_SNAKE_CASE  ,	truth_transform=__SCREAMING_SNAKE_CASE  ,	hypothesis_transform=__SCREAMING_SNAKE_CASE  ,	)["wer"]

           __a		 =       0
           __a		 =       0
           for prediction, reference in zip(__SCREAMING_SNAKE_CASE  ,	__SCREAMING_SNAKE_CASE):
               __a		 =       jiwer.compute_measures(
                   __SCREAMING_SNAKE_CASE  ,	__SCREAMING_SNAKE_CASE  ,	truth_transform=__SCREAMING_SNAKE_CASE  ,	hypothesis_transform=__SCREAMING_SNAKE_CASE  ,	)
               incorrect += measures["substitutions"] + measures["deletions"] + measures["insertions"]
               total += measures["substitutions"] + measures["deletions"] + measures["hits"]

           return incorrect / total





