






'''simple docstring'''






from abc import ABC, abstractmethod
from typing import Optional, Union

from .. import Dataset, DatasetDict, Features, IterableDataset, IterableDatasetDict, NamedSplit
from ..utils.typing import NestedDataStructureLike, PathLike




class a_    (    UpperCamelCase_							):







			def __init__(self					,   __a = None					,   __a = None					,   __a = None					,   __a = None					,   __a = False					,   __a = False					,   __a = None					,   **__a					,   )			->      List[str]:
						"""simple docstring"""






						__snake_case				:      Union[str, Any]     							= path_or_paths
						__snake_case				:      Tuple     							= split if split or isinstance(__a					,   __a) else 'train'
						__snake_case				:      List[str]     							= features
						__snake_case				:      List[Any]     							= cache_dir
						__snake_case				:      Any     							= keep_in_memory
						__snake_case				:      Optional[Any]     							= streaming
						__snake_case				:      Optional[Any]     							= num_proc
						__snake_case				:      Tuple     							= kwargs







			@abstractmethod
			def     SCREAMING_SNAKE_CASE__					(self)			->      Union[Dataset, DatasetDict, IterableDataset, IterableDatasetDict]:
						"""simple docstring"""






						pass




class a_    (    UpperCamelCase_							):







			def __init__(self					,   __a = None					,   __a = None					,   __a = False					,   __a = False					,   __a = None					,   **__a					,   )			->      Any:
						"""simple docstring"""






						__snake_case				:      List[str]     							= features
						__snake_case				:      List[str]     							= cache_dir
						__snake_case				:      Any     							= keep_in_memory
						__snake_case				:      Optional[int]     							= streaming
						__snake_case				:      List[Any]     							= num_proc
						__snake_case				:      Dict     							= kwargs







			@abstractmethod
			def     SCREAMING_SNAKE_CASE__					(self)			->      Union[Dataset, IterableDataset]:
						"""simple docstring"""






						pass







'''simple docstring'''






from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload




class a_    :







   def __init__(self					,   __a = None)			->      None:
      """simple docstring"""






      if components is None:
         __snake_case				:      List[str]     							= []
      __snake_case				:      Optional[int]     							= list(__a)







   def __len__(self)			->      int:
      """simple docstring"""






      return len(self.__components)







   def __str__(self)			->      str:
      """simple docstring"""






      return "(" + ",".join(map(__a					,   self.__components)) + ")"







   def __add__(self					,   __a)			->      Vector:
      """simple docstring"""






      __snake_case				:      Optional[Any]     							= len(self)
      if size == len(__a):
         __snake_case				:      Optional[int]     							= [self.__components[i] + other.component(__a) for i in range(__a)]
         return Vector(__a)
      else:
         raise Exception('must have the same size')







   def __sub__(self					,   __a)			->      Vector:
      """simple docstring"""






      __snake_case				:      Optional[Any]     							= len(self)
      if size == len(__a):
         __snake_case				:      Optional[int]     							= [self.__components[i] - other.component(__a) for i in range(__a)]
         return Vector(__a)
      else:  # error case
         raise Exception('must have the same size')







   @overload
   def __mul__(self					,   __a)			->      Vector:
      """simple docstring"""






      ...







   @overload
   def __mul__(self					,   __a)			->      float:
      """simple docstring"""






      ...







   def __mul__(self					,   __a)			->      float | Vector:
      """simple docstring"""






      if isinstance(__a					,   (float, int)):
         __snake_case				:      str     							= [c * other for c in self.__components]
         return Vector(__a)
      elif isinstance(__a					,   __a) and len(self) == len(__a):
         __snake_case				:      List[Any]     							= len(self)
         __snake_case				:      Dict     							= [self.__components[i] * other.component(__a) for i in range(__a)]
         return sum(__a)
      else:  # error case
         raise Exception('invalid operand!')







   def     SCREAMING_SNAKE_CASE__					(self)			->      Vector:
      """simple docstring"""






      return Vector(self.__components)







   def     SCREAMING_SNAKE_CASE__					(self					,   __a)			->      float:
      """simple docstring"""






      if isinstance(__a					,   __a) and -len(self.__components) <= i < len(self.__components):
         return self.__components[i]
      else:
         raise Exception('index out of range')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      None:
      """simple docstring"""






      assert -len(self.__components) <= pos < len(self.__components)
      __snake_case				:      int     							= value







   def     SCREAMING_SNAKE_CASE__					(self)			->      float:
      """simple docstring"""






      if len(self.__components) == 0:
         raise Exception('Vector is empty')
      __snake_case				:      Tuple     							= [c**2 for c in self.__components]
      return math.sqrt(sum(__a))







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a = False)			->      float:
      """simple docstring"""






      __snake_case				:      Tuple     							= self * other
      __snake_case				:      Optional[int]     							= self.euclidean_length() * other.euclidean_length()
      if deg:
         return math.degrees(math.acos(num / den))
      else:
         return math.acos(num / den)




def        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> Vector:







   """simple docstring"""
   assert isinstance(A  ,		A  )
   return Vector([0] * dimension  )




def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  )    -> Vector:







   """simple docstring"""
   assert isinstance(A  ,		A  ) and (isinstance(A  ,		A  ))
   __snake_case				:      Any     							= [0] * dimension
   __snake_case				:      int     							= 1
   return Vector(A  )




def        _SCREAMING_SNAKE_CASE  (				A  :       float  ,		A  :       Vector  ,		A  :       Vector  )    -> Vector:







   """simple docstring"""
   assert (
       isinstance(A  ,		A  )
       and isinstance(A  ,		A  )
       and (isinstance(A  ,		(int, float)  ))
   )
   return x * scalar + y




def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  ,		A  :       int  )    -> Vector:







   """simple docstring"""
   random.seed(A  )
   __snake_case				:      List[Any]     							= [random.randint(A  ,		A  ) for _ in range(A  )]
   return Vector(A  )




class a_    :







   def __init__(self					,   __a					,   __a					,   __a)			->      None:
      """simple docstring"""






      __snake_case				:      Union[str, Any]     							= matrix
      __snake_case				:      int     							= w
      __snake_case				:      str     							= h







   def __str__(self)			->      str:
      """simple docstring"""






      __snake_case				:      Dict     							= ''
      for i in range(self.__height):
         ans += "|"
         for j in range(self.__width):
            if j < self.__width - 1:
               ans += str(self.__matrix[i][j]) + ","
            else:
               ans += str(self.__matrix[i][j]) + "|\n"
      return ans







   def __add__(self					,   __a)			->      Matrix:
      """simple docstring"""






      if self.__width == other.width() and self.__height == other.height():
         __snake_case				:      Tuple     							= []
         for i in range(self.__height):
            __snake_case				:      List[Any]     							= [
                self.__matrix[i][j] + other.component(__a					,   __a)
                for j in range(self.__width)
            ]
            matrix.append(__a)
         return Matrix(__a					,   self.__width					,   self.__height)
      else:
         raise Exception('matrix must have the same dimension!')







   def __sub__(self					,   __a)			->      Matrix:
      """simple docstring"""






      if self.__width == other.width() and self.__height == other.height():
         __snake_case				:      str     							= []
         for i in range(self.__height):
            __snake_case				:      List[str]     							= [
                self.__matrix[i][j] - other.component(__a					,   __a)
                for j in range(self.__width)
            ]
            matrix.append(__a)
         return Matrix(__a					,   self.__width					,   self.__height)
      else:
         raise Exception('matrices must have the same dimension!')







   @overload
   def __mul__(self					,   __a)			->      Matrix:
      """simple docstring"""






      ...







   @overload
   def __mul__(self					,   __a)			->      Vector:
      """simple docstring"""






      ...







   def __mul__(self					,   __a)			->      Vector | Matrix:
      """simple docstring"""






      if isinstance(__a					,   __a):  # matrix-vector
         if len(__a) == self.__width:
            __snake_case				:      Tuple     							= zero_vector(self.__height)
            for i in range(self.__height):
               __snake_case				:      Union[str, Any]     							= [
                   self.__matrix[i][j] * other.component(__a)
                   for j in range(self.__width)
               ]
               ans.change_component(__a					,   sum(__a))
            return ans
         else:
            raise Exception(
                'vector must have the same size as the '
                'number of columns of the matrix!')
      elif isinstance(__a					,   (int, float)):  # matrix-scalar
         __snake_case				:      str     							= [
             [self.__matrix[i][j] * other for j in range(self.__width)]
             for i in range(self.__height)
         ]
         return Matrix(__a					,   self.__width					,   self.__height)
      return None







   def     SCREAMING_SNAKE_CASE__					(self)			->      int:
      """simple docstring"""






      return self.__height







   def     SCREAMING_SNAKE_CASE__					(self)			->      int:
      """simple docstring"""






      return self.__width







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if 0 <= x < self.__height and 0 <= y < self.__width:
         return self.__matrix[x][y]
      else:
         raise Exception('change_component: indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a					,   __a)			->      None:
      """simple docstring"""






      if 0 <= x < self.__height and 0 <= y < self.__width:
         __snake_case				:      List[Any]     							= value
      else:
         raise Exception('change_component: indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      __snake_case				:      List[Any]     							= self.__matrix[:x] + self.__matrix[x + 1 :]
      for i in range(len(__a)):
         __snake_case				:      Tuple     							= minor[i][:y] + minor[i][y + 1 :]
      return Matrix(__a					,   self.__width - 1					,   self.__height - 1).determinant()







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      if 0 <= x < self.__height and 0 <= y < self.__width:
         return (-1) ** (x + y) * self.minor(__a					,   __a)
      else:
         raise Exception('Indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      if self.__height < 1:
         raise Exception('Matrix has no element')
      elif self.__height == 1:
         return self.__matrix[0][0]
      elif self.__height == 2:
         return (
             self.__matrix[0][0] * self.__matrix[1][1]
             - self.__matrix[0][1] * self.__matrix[1][0]
         )
      else:
         __snake_case				:      Any     							= [
             self.__matrix[0][y] * self.cofactor(0					,   __a) for y in range(self.__width)
         ]
         return sum(__a)




def        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> Matrix:







   """simple docstring"""
   __snake_case				:      list[list[float]]     							= [[0] * n for _ in range(A  )]
   return Matrix(A  ,		A  ,		A  )





def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  ,		A  :       int  ,		A  :       int  )    -> Matrix:







   """simple docstring"""
   random.seed(A  )
   __snake_case				:      list[list[float]]     							= [
       [random.randint(A  ,		A  ) for _ in range(A  )] for _ in range(A  )
   ]
   return Matrix(A  ,		A  ,		A  )