





from __future__ import annotations

from typing import Any

class    lowerCAmelCase							:
 def __init__(      self  :      Tuple			,     UpperCAmelCase  :      int			,     UpperCAmelCase  :      int			,     UpperCAmelCase  :      float = 0	)			->	None:
     lowerCamelCase__ ,							lowerCamelCase__    :      str					 =		row, column
     lowerCamelCase__    :      str					 =		[[default_value for c in range(UpperCAmelCase	)] for r in range(UpperCAmelCase	)]
 def __str__(      self  :      str	)			->	str:
     lowerCamelCase__    :      str					 =		F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

     # Make string identifier
     lowerCamelCase__    :      Optional[int]					 =		0
     for row_vector in self.array:
         for obj in row_vector:
             lowerCamelCase__    :      List[Any]					 =		max(UpperCAmelCase			,     len(str(UpperCAmelCase	)	)	)
     lowerCamelCase__    :      List[Any]					 =		F"""%{max_element_length}s"""

     # Make string and return
     def single_line(UpperCAmelCase  :      list[float]	) -> str:
         nonlocal string_format_identifier
         lowerCamelCase__    :      List[Any]					 =		'['
         line += ", ".join(string_format_identifier % (obj,) for obj in row_vector	)
         line += "]"
         return line

     s += "\n".join(single_line(UpperCAmelCase	) for row_vector in self.array	)
     return s
 def __repr__(      self  :      Optional[Any]	)			->	str:
     return str(self	)
 def      A_	(      self  :      Any			,     UpperCAmelCase  :      tuple[int, int]	)			->	bool:
     if not (isinstance(UpperCAmelCase			,     (list, tuple)	) and len(UpperCAmelCase	) == 2):
         return False
     elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
         return False
     else:
         return True
 def __getitem__(      self  :      Any			,     UpperCAmelCase  :      tuple[int, int]	)			->	Any:
     assert self.validate_indicies(UpperCAmelCase	)
     return self.array[loc[0]][loc[1]]
 def __setitem__(      self  :      str			,     UpperCAmelCase  :      tuple[int, int]			,     UpperCAmelCase  :      float	)			->	None:
     assert self.validate_indicies(UpperCAmelCase	)
     lowerCamelCase__    :      Dict					 =		value
 def __add__(      self  :      Optional[Any]			,     UpperCAmelCase  :      Matrix	)			->	Matrix:
     assert isinstance(UpperCAmelCase			,     UpperCAmelCase	)
     assert self.row == another.row and self.column == another.column

     # Add
     lowerCamelCase__    :      List[Any]					 =		Matrix(self.row			,     self.column	)
     for r in range(self.row	):
         for c in range(self.column	):
             lowerCamelCase__    :      Dict					 =		self[r, c] + another[r, c]
     return result
 def __neg__(      self  :      Dict	)			->	Matrix:
     lowerCamelCase__    :      int					 =		Matrix(self.row			,     self.column	)
     for r in range(self.row	):
         for c in range(self.column	):
             lowerCamelCase__    :      List[str]					 =		-self[r, c]
     return result
 def __sub__(      self  :      List[Any]			,     UpperCAmelCase  :      Matrix	)			->	Matrix:
     return self + (-another)
 def __mul__(      self  :      Tuple			,     UpperCAmelCase  :      int | float | Matrix	)			->	Matrix:

     if isinstance(UpperCAmelCase			,     (int, float)	):  # Scalar multiplication
         lowerCamelCase__    :      Union[str, Any]					 =		Matrix(self.row			,     self.column	)
         for r in range(self.row	):
             for c in range(self.column	):
                 lowerCamelCase__    :      Dict					 =		self[r, c] * another
         return result
     elif isinstance(UpperCAmelCase			,     UpperCAmelCase	):  # Matrix multiplication
         assert self.column == another.row
         lowerCamelCase__    :      Optional[int]					 =		Matrix(self.row			,     another.column	)
         for r in range(self.row	):
             for c in range(another.column	):
                 for i in range(self.column	):
                     result[r, c] += self[r, i] * another[i, c]
         return result
     else:
         lowerCamelCase__    :      Any					 =		F"""Unsupported type given for another ({type(UpperCAmelCase	)})"""
         raise TypeError(UpperCAmelCase	)
 def      A_	(      self  :      Optional[Any]	)			->	Matrix:
     lowerCamelCase__    :      str					 =		Matrix(self.column			,     self.row	)
     for r in range(self.row	):
         for c in range(self.column	):
             lowerCamelCase__    :      Tuple					 =		self[r, c]
     return result







 def      A_	(      self  :      Tuple			,     UpperCAmelCase  :      Matrix			,     UpperCAmelCase  :      Matrix	)			->	Any:
     assert isinstance(UpperCAmelCase			,     UpperCAmelCase	) and isinstance(UpperCAmelCase			,     UpperCAmelCase	)
     assert self.row == self.column == u.row == v.row  # u, v should be column vector
     assert u.column == v.column == 1  # u, v should be column vector

     # Calculate
     lowerCamelCase__    :      Any					 =		v.transpose()
     lowerCamelCase__    :      Dict					 =		(v_t * self * u)[0, 0] + 1
     if numerator_factor == 0:
         return None  # It's not invertable
     return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":


    def        SCREAMING_SNAKE_CASE      (       )			->     None:
        # a^(-1)
        lowerCamelCase__    :      str					 =		Matrix(3						,	3						,	0 )
        for i in range(3 ):
            lowerCamelCase__    :      str					 =		1
        print(F"""a^(-1) is {ainv}""" )
        # u, v
        lowerCamelCase__    :      Any					 =		Matrix(3						,	1						,	0 )
        lowerCamelCase__ ,							lowerCamelCase__ ,							lowerCamelCase__    :      Tuple					 =		1, 2, -3
        lowerCamelCase__    :      Tuple					 =		Matrix(3						,	1						,	0 )
        lowerCamelCase__ ,							lowerCamelCase__ ,							lowerCamelCase__    :      str					 =		4, -2, 5
        print(F"""u is {u}""" )
        print(F"""v is {v}""" )
        print(F"""uv^T is {u * v.transpose()}""" )
        # Sherman Morrison
        print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(_UpperCAmelCase						,	_UpperCAmelCase )}""" )


    def        SCREAMING_SNAKE_CASE      (       )			->     None:
        import doctest

        doctest.testmod()


    testa()












from __future__ import annotations

from typing import Any


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase )			->     None:
    create_state_space_tree(_UpperCAmelCase						,	[]						,	0 )


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase )			->     None:

    if index == len(_UpperCAmelCase ):
        print(_UpperCAmelCase )
        return

    create_state_space_tree(_UpperCAmelCase						,	_UpperCAmelCase						,	index + 1 )
    current_subsequence.append(sequence[index] )
    create_state_space_tree(_UpperCAmelCase						,	_UpperCAmelCase						,	index + 1 )
    current_subsequence.pop()


if __name__ == "__main__":
    _UpperCAmelCase				:       list[Any]	   =				[3, 1, 2, 4]
    generate_all_subsequences(seq)

    seq.clear()
    seq.extend(["""A""", """B""", """C"""])
    generate_all_subsequences(seq)





