





"""simple docstring"""



from __future__ import annotations

import math







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  list						)       ->list:



    '''simple docstring'''







    if len(snake_case_						) != 2 or len(a[0]						) != 2 or len(snake_case_						) != 2 or len(b[0]						) != 2:
        raise Exception('''Matrices are not 2x2'''						)
    __A   :						str									=					[
        [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
        [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
    ]
    return new_matrix







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  list						)       ->Union[str, Any]:



    '''simple docstring'''







    return [
        [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
        for row in range(len(snake_case_						)						)
    ]







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  list						)       ->str:



    '''simple docstring'''







    return [
        [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]						)						)]
        for row in range(len(snake_case_						)						)
    ]







def 		__lowercase					(       snake_case_  :  list						)       ->tuple[list, list, list, list]:



    '''simple docstring'''







    if len(snake_case_						) % 2 != 0 or len(a[0]						) % 2 != 0:
        raise Exception('''Odd matrices are not supported!'''						)

    __A   :						Union[str, Any]									=					len(snake_case_						)
    __A   :						int									=					matrix_length // 2

    __A   :						str									=					[[a[i][j] for j in range(snake_case_    ,snake_case_						)] for i in range(snake_case_						)]
    __A   :						List[str]									=					[
        [a[i][j] for j in range(snake_case_    ,snake_case_						)] for i in range(snake_case_    ,snake_case_						)
    ]

    __A   :						Optional[Any]									=					[[a[i][j] for j in range(snake_case_						)] for i in range(snake_case_						)]
    __A   :						int									=					[[a[i][j] for j in range(snake_case_						)] for i in range(snake_case_    ,snake_case_						)]

    return top_left, top_right, bot_left, bot_right







def 		__lowercase					(       snake_case_  :  list						)       ->tuple[int, int]:



    '''simple docstring'''







    return len(snake_case_						), len(matrix[0]						)







def 		__lowercase					(       snake_case_  :  list						)       ->None:



    '''simple docstring'''







    print('''\n'''.join(str(snake_case_						) for line in matrix						)						)







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  list						)       ->list:



    '''simple docstring'''







    if matrix_dimensions(snake_case_						) == (2, 2):
        return default_matrix_multiplication(snake_case_    ,snake_case_						)

    __A			,	__A			,	__A			,	__A   :						Dict									=					split_matrix(snake_case_						)
    __A			,	__A			,	__A			,	__A   :						int									=					split_matrix(snake_case_						)

    __A   :						Tuple									=					actual_strassen(snake_case_    ,matrix_subtraction(snake_case_    ,snake_case_						)						)
    __A   :						int									=					actual_strassen(matrix_addition(snake_case_    ,snake_case_						)    ,snake_case_						)
    __A   :						Any									=					actual_strassen(matrix_addition(snake_case_    ,snake_case_						)    ,snake_case_						)
    __A   :						Optional[int]									=					actual_strassen(snake_case_    ,matrix_subtraction(snake_case_    ,snake_case_						)						)
    __A   :						List[str]									=					actual_strassen(matrix_addition(snake_case_    ,snake_case_						)    ,matrix_addition(snake_case_    ,snake_case_						)						)
    __A   :						str									=					actual_strassen(matrix_subtraction(snake_case_    ,snake_case_						)    ,matrix_addition(snake_case_    ,snake_case_						)						)
    __A   :						Union[str, Any]									=					actual_strassen(matrix_subtraction(snake_case_    ,snake_case_						)    ,matrix_addition(snake_case_    ,snake_case_						)						)

    __A   :						str									=					matrix_addition(matrix_subtraction(matrix_addition(snake_case_    ,snake_case_						)    ,snake_case_						)    ,snake_case_						)
    __A   :						Any									=					matrix_addition(snake_case_    ,snake_case_						)
    __A   :						List[str]									=					matrix_addition(snake_case_    ,snake_case_						)
    __A   :						str									=					matrix_subtraction(matrix_subtraction(matrix_addition(snake_case_    ,snake_case_						)    ,snake_case_						)    ,snake_case_						)

    # construct the new matrix from our 4 quadrants
    __A   :						List[Any]									=					[]
    for i in range(len(snake_case_						)						):
        new_matrix.append(top_left[i] + top_right[i]						)
    for i in range(len(snake_case_						)						):
        new_matrix.append(bot_left[i] + bot_right[i]						)
    return new_matrix







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  list						)       ->list:



    '''simple docstring'''







    if matrix_dimensions(snake_case_						)[1] != matrix_dimensions(snake_case_						)[0]:
        __A   :						Any									=					(
            '''Unable to multiply these matrices, please check the dimensions.\n'''
            F"""Matrix A: {matrixa}\n"""
            F"""Matrix B: {matrixa}"""
        )
        raise Exception(snake_case_						)
    __A   :						Optional[Any]									=					matrix_dimensions(snake_case_						)
    __A   :						int									=					matrix_dimensions(snake_case_						)

    if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
        return [matrixa, matrixa]

    __A   :						Any									=					max(*snake_case_    ,*snake_case_						)
    __A   :						List[Any]									=					int(math.pow(2    ,math.ceil(math.loga(snake_case_						)						)						)						)
    __A   :						Optional[Any]									=					matrixa
    __A   :						List[str]									=					matrixa

    # Adding zeros to the matrices so that the arrays dimensions are the same and also
    # power of 2
    for i in range(0    ,snake_case_						):
        if i < dimensiona[0]:
            for _ in range(dimensiona[1]    ,snake_case_						):
                new_matrixa[i].append(0						)
        else:
            new_matrixa.append([0] * maxim						)
        if i < dimensiona[0]:
            for _ in range(dimensiona[1]    ,snake_case_						):
                new_matrixa[i].append(0						)
        else:
            new_matrixa.append([0] * maxim						)

    __A   :						str									=					actual_strassen(snake_case_    ,snake_case_						)

    # Removing the additional zeros
    for i in range(0    ,snake_case_						):
        if i < dimensiona[0]:
            for _ in range(dimensiona[1]    ,snake_case_						):
                final_matrix[i].pop()
        else:
            final_matrix.pop()
    return final_matrix


if __name__ == "__main__":
       a_			=      [
           [2, 3, 4, 5],
           [6, 4, 3, 1],
           [2, 3, 6, 7],
           [3, 1, 2, 4],
           [2, 3, 4, 5],
           [6, 4, 3, 1],
           [2, 3, 6, 7],
           [3, 1, 2, 4],
           [2, 3, 4, 5],
           [6, 2, 3, 1],
       ]
       a_			=      [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
       print(strassen(matrixa, matrixa))











"""simple docstring"""



from pathlib import PurePosixPath
from typing import Optional

import fsspec
from fsspec import AbstractFileSystem
from huggingface_hub.hf_api import DatasetInfo

from ..utils.file_utils import get_authentication_headers_for_url
from ..utils.hub import hf_hub_url






class 		__snake_case (		SCREAMING_SNAKE_CASE__					):





 """simple docstring"""


 _lowerCamelCase				=					""""""
 _lowerCamelCase				=					"""hf-legacy"""  # "hf://"" is reserved for hffs

 def __init__(   self ,						__lowerCamelCase = None ,						__lowerCamelCase = None ,						**__lowerCamelCase ,						):



     '''simple docstring'''




     super().__init__(self ,						**__lowerCamelCase  )
     __A   :						int									=					repo_info
     __A   :						Optional[int]									=					token
     __A   :						int									=					None

 def  UpperCamelCase__(   self  ):



     '''simple docstring'''




     if self.dir_cache is None:
         __A   :						int									=					{}
         for hf_file in self.repo_info.siblings:
             # TODO(QL): add sizes
             __A   :						Tuple									=					{
                 '''name''': hf_file.rfilename,
                 '''size''': None,
                 '''type''': '''file''',
             }
             self.dir_cache.update(
                 {
                     str(__lowerCamelCase  ): {'''name''': str(__lowerCamelCase  ), '''size''': None, '''type''': '''directory'''}
                     for d in list(PurePosixPath(hf_file.rfilename  ).parents  )[:-1]
                 }  )

 def  UpperCamelCase__(   self ,						__lowerCamelCase ,						__lowerCamelCase = "rb" ,						**__lowerCamelCase ,						):



     '''simple docstring'''




     if not isinstance(self.repo_info ,						__lowerCamelCase  ):
         raise NotImplementedError(F"""Open is only implemented for dataset repositories, but got {self.repo_info}"""  )
     __A   :						Union[str, Any]									=					hf_hub_url(self.repo_info.id ,						__lowerCamelCase ,						revision=self.repo_info.sha  )
     return fsspec.open(
         __lowerCamelCase ,						mode=__lowerCamelCase ,						headers=get_authentication_headers_for_url(__lowerCamelCase ,						use_auth_token=self.token  ) ,						client_kwargs={'''trust_env''': True} ,						).open()

 def  UpperCamelCase__(   self ,						__lowerCamelCase ,						**__lowerCamelCase  ):



     '''simple docstring'''




     self._get_dirs()
     __A   :						Optional[Any]									=					self._strip_protocol(__lowerCamelCase  )
     if path in self.dir_cache:
         return self.dir_cache[path]
     else:
         raise FileNotFoundError(__lowerCamelCase  )







 def  UpperCamelCase__(   self ,						__lowerCamelCase ,						__lowerCamelCase=False ,						**__lowerCamelCase  ):



     '''simple docstring'''




     self._get_dirs()
     __A   :						Any									=					PurePosixPath(path.strip('''/'''  )  )
     __A   :						Any									=					{}
     for p, f in self.dir_cache.items():
         __A   :						List[Any]									=					PurePosixPath(p.strip('''/'''  )  )
         __A   :						Dict									=					p.parent
         if root == path:
             __A   :						Union[str, Any]									=					f
     __A   :						List[str]									=					list(paths.values()  )
     if detail:
         return out
     else:
         return sorted(f['''name'''] for f in out  )




