


'''simple docstring'''



from __future__ import annotations





class    UpperCAmelCase_  :





    """simple docstring"""






    def __init__(							self			,     SCREAMING_SNAKE_CASE_	)				->     Dict:
         __lowerCamelCase   :	Optional[Any]								=		TypeError(
             'Matrices must be formed from a list of zero or more lists containing at '
             'least one and the same number of values, each of which must be of type '
             'int or float.'	)
         if len(SCREAMING_SNAKE_CASE_	) != 0:
              __lowerCamelCase   :	List[str]								=		len(rows[0]	)
              if cols == 0:
                   raise error
              for row in rows:
                   if len(SCREAMING_SNAKE_CASE_	) != cols:
                        raise error
                   for value in row:
                        if not isinstance(SCREAMING_SNAKE_CASE_			,     (int, float)	):
                             raise error
              __lowerCamelCase   :	List[str]								=		rows
         else:
              __lowerCamelCase   :	Optional[int]								=		[]







    def       lowercase_				(							self	)				->     list[list[int]]:
         return [[row[i] for row in self.rows] for i in range(len(self.rows[0]	)	)]







    @property
    def       lowercase_				(							self	)				->     int:
         return len(self.rows	)







    @property
    def       lowercase_				(							self	)				->     int:
         return len(self.rows[0]	)







    @property
    def       lowercase_				(							self	)				->     tuple[int, int]:
         return (self.num_rows, self.num_columns)







    @property
    def       lowercase_				(							self	)				->     bool:
         return self.order[0] == self.order[1]







    def       lowercase_				(							self	)				->     Matrix:
         __lowerCamelCase   :	Any								=		[
             [0 if column_num != row_num else 1 for column_num in range(self.num_rows	)]
             for row_num in range(self.num_rows	)
         ]
         return Matrix(SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self	)				->     int:
         if not self.is_square:
              return 0
         if self.order == (0, 0):
              return 1
         if self.order == (1, 1):
              return int(self.rows[0][0]	)
         if self.order == (2, 2):
              return int(
                  (self.rows[0][0] * self.rows[1][1])
                  - (self.rows[0][1] * self.rows[1][0])	)
         else:
              return sum(
                  self.rows[0][column] * self.cofactors().rows[0][column]
                  for column in range(self.num_columns	)	)







    def       lowercase_				(							self	)				->     bool:
         return bool(self.determinant()	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     int:
         __lowerCamelCase   :	List[str]								=		[
             [
                 self.rows[other_row][other_column]
                 for other_column in range(self.num_columns	)
                 if other_column != column
             ]
             for other_row in range(self.num_rows	)
             if other_row != row
         ]
         return Matrix(SCREAMING_SNAKE_CASE_	).determinant()







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     int:
         if (row + column) % 2 == 0:
              return self.get_minor(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
         return -1 * self.get_minor(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self	)				->     Matrix:
         return Matrix(
             [
                 [self.get_minor(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	) for column in range(self.num_columns	)]
                 for row in range(self.num_rows	)
             ]	)







    def       lowercase_				(							self	)				->     Matrix:
         return Matrix(
             [
                 [
                     self.minors().rows[row][column]
                     if (row + column) % 2 == 0
                     else self.minors().rows[row][column] * -1
                     for column in range(self.minors().num_columns	)
                 ]
                 for row in range(self.minors().num_rows	)
             ]	)







    def       lowercase_				(							self	)				->     Matrix:
         __lowerCamelCase   :	List[Any]								=		[
             [self.cofactors().rows[column][row] for column in range(self.num_columns	)]
             for row in range(self.num_rows	)
         ]
         return Matrix(SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self	)				->     Matrix:
         __lowerCamelCase   :	List[str]								=		self.determinant()
         if not determinant:
              raise TypeError('Only matrices with a non-zero determinant have an inverse'	)
         return self.adjugate() * (1 / determinant)







    def __repr__(							self	)				->     str:
         return str(self.rows	)







    def __str__(							self	)				->     str:
         if self.num_rows == 0:
              return "[]"
         if self.num_rows == 1:
              return "[[" + ". ".join(str(self.rows[0]	)	) + "]]"
         return (
             "["
             + "\n ".join(
                 [
                     '[' + '. '.join([str(SCREAMING_SNAKE_CASE_	) for value in row]	) + '.]'
                     for row in self.rows
                 ]	)
             + "]"
         )







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = None	)				->     None:
         __lowerCamelCase   :	Union[str, Any]								=		TypeError('Row must be a list containing all ints and/or floats'	)
         if not isinstance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	):
              raise type_error
         for value in row:
              if not isinstance(SCREAMING_SNAKE_CASE_			,     (int, float)	):
                   raise type_error
         if len(SCREAMING_SNAKE_CASE_	) != self.num_columns:
              raise ValueError(
                  'Row must be equal in length to the other rows in the matrix'	)
         if position is None:
              self.rows.append(SCREAMING_SNAKE_CASE_	)
         else:
              __lowerCamelCase   :	str								=		self.rows[0:position] + [row] + self.rows[position:]







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = None	)				->     None:
         __lowerCamelCase   :	Any								=		TypeError(
             'Column must be a list containing all ints and/or floats'	)
         if not isinstance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	):
              raise type_error
         for value in column:
              if not isinstance(SCREAMING_SNAKE_CASE_			,     (int, float)	):
                   raise type_error
         if len(SCREAMING_SNAKE_CASE_	) != self.num_rows:
              raise ValueError(
                  'Column must be equal in length to the other columns in the matrix'	)
         if position is None:
              __lowerCamelCase   :	Tuple								=		[self.rows[i] + [column[i]] for i in range(self.num_rows	)]
         else:
              __lowerCamelCase   :	Union[str, Any]								=		[
                  self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                  for i in range(self.num_rows	)
              ]







    def __eq__(							self			,     SCREAMING_SNAKE_CASE_	)				->     bool:
         if not isinstance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	):
              return NotImplemented
         return self.rows == other.rows







    def __ne__(							self			,     SCREAMING_SNAKE_CASE_	)				->     bool:
         return not self == other







    def __neg__(							self	)				->     Matrix:
         return self * -1







    def __add__(							self			,     SCREAMING_SNAKE_CASE_	)				->     Matrix:
         if self.order != other.order:
              raise ValueError('Addition requires matrices of the same order'	)
         return Matrix(
             [
                 [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns	)]
                 for i in range(self.num_rows	)
             ]	)







    def __sub__(							self			,     SCREAMING_SNAKE_CASE_	)				->     Matrix:
         if self.order != other.order:
              raise ValueError('Subtraction requires matrices of the same order'	)
         return Matrix(
             [
                 [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns	)]
                 for i in range(self.num_rows	)
             ]	)







    def __mul__(							self			,     SCREAMING_SNAKE_CASE_	)				->     Matrix:
         if isinstance(SCREAMING_SNAKE_CASE_			,     (int, float)	):
              return Matrix(
                  [[int(element * other	) for element in row] for row in self.rows]	)
         elif isinstance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	):
              if self.num_columns != other.num_rows:
                   raise ValueError(
                       'The number of columns in the first matrix must '
                       'be equal to the number of rows in the second'	)
              return Matrix(
                  [
                      [Matrix.dot_product(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	) for column in other.columns()]
                      for row in self.rows
                  ]	)
         else:
              raise TypeError(
                  'A Matrix can only be multiplied by an int, float, or another matrix'	)







    def __pow__(							self			,     SCREAMING_SNAKE_CASE_	)				->     Matrix:
         if not isinstance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	):
              raise TypeError('A Matrix can only be raised to the power of an int'	)
         if not self.is_square:
              raise ValueError('Only square matrices can be raised to a power'	)
         if other == 0:
              return self.identity()
         if other < 0:
              if self.is_invertable():
                   return self.inverse() ** (-other)
              raise ValueError(
                  'Only invertable matrices can be raised to a negative power'	)
         __lowerCamelCase   :	Dict								=		self
         for _ in range(other - 1	):
              result *= self
         return result







    @classmethod
    def       lowercase_				(							cls			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     int:
         return sum(row[i] * column[i] for i in range(len(SCREAMING_SNAKE_CASE_	)	)	)


if __name__ == "__main__":
      import doctest

      doctest.testmod()










'''simple docstring'''



import unittest

from knapsack import knapsack as k





class    UpperCAmelCase_  (unittest.TestCase  ):





    """simple docstring"""






    def       lowercase_				(							self	)				->     Optional[Any]:
         __lowerCamelCase   :	int								=		0
         __lowerCamelCase   :	Union[str, Any]								=		[0]
         __lowerCamelCase   :	Any								=		[0]
         __lowerCamelCase   :	Union[str, Any]								=		len(SCREAMING_SNAKE_CASE_	)
         self.assertEqual(k.knapsack(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)			,     0	)

         __lowerCamelCase   :	List[str]								=		[60]
         __lowerCamelCase   :	Union[str, Any]								=		[10]
         __lowerCamelCase   :	List[Any]								=		len(SCREAMING_SNAKE_CASE_	)
         self.assertEqual(k.knapsack(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)			,     0	)







    def       lowercase_				(							self	)				->     List[str]:
         __lowerCamelCase   :	Optional[int]								=		3
         __lowerCamelCase   :	int								=		[1, 2, 3]
         __lowerCamelCase   :	str								=		[3, 2, 1]
         __lowerCamelCase   :	Union[str, Any]								=		len(SCREAMING_SNAKE_CASE_	)
         self.assertEqual(k.knapsack(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)			,     5	)







    def       lowercase_				(							self	)				->     int:
         __lowerCamelCase   :	Optional[int]								=		50
         __lowerCamelCase   :	List[str]								=		[60, 1_00, 1_20]
         __lowerCamelCase   :	List[str]								=		[10, 20, 30]
         __lowerCamelCase   :	List[str]								=		len(SCREAMING_SNAKE_CASE_	)
         self.assertEqual(k.knapsack(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)			,     2_20	)


if __name__ == "__main__":
      unittest.main()






