



"""simple docstring"""






from __future__ import annotations

from typing import Any

class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





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



					def __str__( self							:						Any  )->      str:
								lowerCamelCase__	:	Optional[Any]				=F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

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

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

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



					def __repr__( self							:						List[Any]  )->      str:
								return str(self  )



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



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



					def __setitem__( self							:						Tuple,						lowerCamelCase							:						tuple[int, int],						lowerCamelCase							:						float  )->      None:
								assert self.validate_indicies(__a  )
								lowerCamelCase__	:	List[Any]				=value



					def __add__( self							:						str,						lowerCamelCase							:						Matrix  )->      Matrix:
								assert isinstance(__a,						__a  )
								assert self.row == another.row and self.column == another.column

								# Add
								lowerCamelCase__	:	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							:						str  )->      Matrix:
								lowerCamelCase__	:	List[str]				=Matrix(self.row,						self.column  )
								for r in range(self.row  ):
											for c in range(self.column  ):
														lowerCamelCase__	:	Tuple				=-self[r, c]
								return result



					def __sub__( self							:						Any,						lowerCamelCase							:						Matrix  )->      Matrix:
								return self + (-another)



					def __mul__( self							:						Dict,						lowerCamelCase							:						int | float | Matrix  )->      Matrix:

								if isinstance(__a,						(int, float)  ):  # Scalar multiplication
											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
											return result
								elif isinstance(__a,						__a  ):  # Matrix multiplication
											assert self.column == another.row
											lowerCamelCase__	:	Union[str, Any]				=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__	:	int				=F'''Unsupported type given for another ({type(__a  )})'''
											raise TypeError(__a  )



					def 	snake_case ( self							:						List[Any]  )->      Matrix:
								lowerCamelCase__	:	Union[str, Any]				=Matrix(self.column,						self.row  )
								for r in range(self.row  ):
											for c in range(self.column  ):
														lowerCamelCase__	:	Union[str, Any]				=self[r, c]
								return result




					def 	snake_case ( self							:						Optional[int],						lowerCamelCase							:						Matrix,						lowerCamelCase							:						Matrix  )->      Any:
								assert isinstance(__a,						__a  ) and isinstance(__a,						__a  )
								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__	:	int				=v.transpose()
								lowerCamelCase__	:	Optional[int]				=(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   snake_case__     (	):
					"""simple docstring"""
					lowerCamelCase__	:	str				=Matrix(3							,	3							,	0			)
					for i in range(3			):
								lowerCamelCase__	:	Dict				=1
					print(f'''a^(-1) is {ainv}'''			)
					# u, v
					lowerCamelCase__	:	str				=Matrix(3							,	1							,	0			)
					lowerCamelCase__	:	Any				=1, 2, -3
					lowerCamelCase__	:	List[str]				=Matrix(3							,	1							,	0			)
					lowerCamelCase__	:	List[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(lowercase_							,	lowercase_			)}'''			)






		def   snake_case__     (	):
					"""simple docstring"""
					import doctest

					doctest.testmod()

		testa()









"""simple docstring"""






from __future__ import annotations

from collections.abc import Iterator

class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					def __init__( self							:						str,						lowerCamelCase							:						int  )->      None:
								lowerCamelCase__	:	str				=value
								lowerCamelCase__	:	Node | None				=None
								lowerCamelCase__	:	Node | None				=None





class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					def __init__( self							:						int,						lowerCamelCase							:						Node  )->      None:
								lowerCamelCase__	:	Any				=tree



					def 	snake_case ( self							:						str,						lowerCamelCase							:						Node | None  )->      int:
								if node is None:
											return 0
								return node.value + (
								    self.depth_first_search(node.left  ) + self.depth_first_search(node.right  )
								)




					def __iter__( self							:						Dict  )->      Iterator[int]:
								yield self.depth_first_search(self.tree  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




