



from __future__ import annotations

from typing import Any


class 	lowerCamelCase__	:



 """simple docstring"""

 def __init__(    self					:					List[str]			,						__lowerCAmelCase					:					int			,						__lowerCAmelCase					:					int			,						__lowerCAmelCase					:					float = 0      )   ->	None:
    _A  ,    _A      =       row, column
    _A      =       [[default_value for c in range(__lowerCAmelCase      )] for r in range(__lowerCAmelCase      )]

 def __str__(    self					:					Any      )   ->	str:
    _A      =       f'''Matrix consist of {self.row} rows and {self.column} columns\n'''

    # Make string identifier
    _A      =       0
    for row_vector in self.array:
       for obj in row_vector:
          _A      =       max(__lowerCAmelCase			,						len(str(__lowerCAmelCase      )      )      )
    _A      =       f'''%{max_element_length}s'''

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

    s += "\n".join(single_line(__lowerCAmelCase      ) for row_vector in self.array      )
    return s

 def __repr__(    self					:					Dict      )   ->	str:
    return str(self      )

 def     snake_case_      (    self					:					Optional[int]			,						__lowerCAmelCase					:					tuple[int, int]      )   ->	bool:
    if not (isinstance(__lowerCAmelCase			,						(list, tuple)      ) and len(__lowerCAmelCase      ) == 2):
       return False
    elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
       return False
    else:
       return True

 def __getitem__(    self					:					int			,						__lowerCAmelCase					:					tuple[int, int]      )   ->	Any:
    assert self.validate_indicies(__lowerCAmelCase      )
    return self.array[loc[0]][loc[1]]

 def __setitem__(    self					:					int			,						__lowerCAmelCase					:					tuple[int, int]			,						__lowerCAmelCase					:					float      )   ->	None:
    assert self.validate_indicies(__lowerCAmelCase      )
    _A      =       value

 def __add__(    self					:					int			,						__lowerCAmelCase					:					Matrix      )   ->	Matrix:
    assert isinstance(__lowerCAmelCase			,						__lowerCAmelCase      )
    assert self.row == another.row and self.column == another.column

    # Add
    _A      =       Matrix(self.row			,						self.column      )
    for r in range(self.row      ):
       for c in range(self.column      ):
          _A      =       self[r, c] + another[r, c]
    return result

 def __neg__(    self					:					Optional[Any]      )   ->	Matrix:
    _A      =       Matrix(self.row			,						self.column      )
    for r in range(self.row      ):
       for c in range(self.column      ):
          _A      =       -self[r, c]
    return result

 def __sub__(    self					:					Tuple			,						__lowerCAmelCase					:					Matrix      )   ->	Matrix:
    return self + (-another)

 def __mul__(    self					:					Optional[int]			,						__lowerCAmelCase					:					int | float | Matrix      )   ->	Matrix:

    if isinstance(__lowerCAmelCase			,						(int, float)      ):  # Scalar multiplication
       _A      =       Matrix(self.row			,						self.column      )
       for r in range(self.row      ):
          for c in range(self.column      ):
             _A      =       self[r, c] * another
       return result
    elif isinstance(__lowerCAmelCase			,						__lowerCAmelCase      ):  # Matrix multiplication
       assert self.column == another.row
       _A      =       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:
       _A      =       f'''Unsupported type given for another ({type(__lowerCAmelCase      )})'''
       raise TypeError(__lowerCAmelCase      )

 def     snake_case_      (    self					:					str      )   ->	Matrix:
    _A      =       Matrix(self.column			,						self.row      )
    for r in range(self.row      ):
       for c in range(self.column      ):
          _A      =       self[r, c]
    return result

 def     snake_case_      (    self					:					List[Any]			,						__lowerCAmelCase					:					Matrix			,						__lowerCAmelCase					:					Matrix      )   ->	Any:
    assert isinstance(__lowerCAmelCase			,						__lowerCAmelCase      ) and isinstance(__lowerCAmelCase			,						__lowerCAmelCase      )
    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
    _A      =       v.transpose()
    _A      =       (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)
      _A      =       Matrix(3	,   3	,   0				)
      for i in range(3				):
         _A      =       1
      print(F'''a^(-1) is {ainv}'''				)
      # u, v
      _A      =       Matrix(3	,   1	,   0				)
      _A  ,    _A  ,    _A      =       1, 2, -3
      _A      =       Matrix(3	,   1	,   0				)
      _A  ,    _A  ,    _A      =       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(_snake_case	,   _snake_case				)}'''				)

   def 	SCREAMING_SNAKE_CASE_							(	)  ->     None:
      import doctest

      doctest.testmod()


   testa()








from __future__ import annotations

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:dict	,   _snake_case	:str				)  ->     set[str]:
   _A  ,    _A      =       set(_snake_case				), [start]

   while stack:
      _A      =       stack.pop()
      explored.add(_snake_case				)
      # Differences from BFS:
      # 1) pop last element instead of first one
      # 2) add adjacent elements to stack without exploring them
      for adj in reversed(graph[v]				):
         if adj not in explored:
            stack.append(_snake_case				)
   return explored


UpperCAmelCase_		 =					{
    """A""": ["""B""", """C""", """D"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F"""],
    """D""": ["""B""", """D"""],
    """E""": ["""B""", """F"""],
    """F""": ["""C""", """E""", """G"""],
    """G""": ["""F"""],
}

if __name__ == "__main__":
   import doctest

   doctest.testmod()
   print(depth_first_search(G, """A"""))



