





def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):

				def update_area_of_max_square(__lowerCAmelCase	,			__lowerCAmelCase ) -> int:
								# BASE CASE
								if row >= rows or col >= cols:
												return 0

								_snake_case :			List[str]  						=   update_area_of_max_square(lowerCamelCase_	,			col + 1 )
								_snake_case :			Dict  						=   update_area_of_max_square(row + 1	,			col + 1 )
								_snake_case :			Any  						=   update_area_of_max_square(row + 1	,			lowerCamelCase_ )

								if mat[row][col]:
												_snake_case :			Dict  						=   1 + min([right, diagonal, down] )
												_snake_case :			Optional[int]  						=   max(largest_square_area[0]	,			lowerCamelCase_ )
												return sub_problem_sol
								else:
												return 0

				_snake_case :			List[str]  						=   [0]
				update_area_of_max_square(0	,			0 )
				return largest_square_area[0]

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):

				def update_area_of_max_square_using_dp_array(
				    __lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ) -> int:
								if row >= rows or col >= cols:
												return 0
								if dp_array[row][col] != -1:
												return dp_array[row][col]

								_snake_case :			List[str]  						=   update_area_of_max_square_using_dp_array(lowerCamelCase_	,			col + 1	,			lowerCamelCase_ )
								_snake_case :			List[Any]  						=   update_area_of_max_square_using_dp_array(row + 1	,			col + 1	,			lowerCamelCase_ )
								_snake_case :			Optional[Any]  						=   update_area_of_max_square_using_dp_array(row + 1	,			lowerCamelCase_	,			lowerCamelCase_ )

								if mat[row][col]:
												_snake_case :			List[Any]  						=   1 + min([right, diagonal, down] )
												_snake_case :			int  						=   max(largest_square_area[0]	,			lowerCamelCase_ )
												_snake_case :			int  						=   sub_problem_sol
												return sub_problem_sol
								else:
												return 0

				_snake_case :			Optional[Any]  						=   [0]
				_snake_case :			List[str]  						=   [[-1] * cols for _ in range(lowerCamelCase_ )]
				update_area_of_max_square_using_dp_array(0	,			0	,			lowerCamelCase_ )

				return largest_square_area[0]

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Union[str, Any]  						=   [[0] * (cols + 1) for _ in range(rows + 1 )]
				_snake_case :			Optional[int]  						=   0
				for row in range(rows - 1	,			-1	,			-1 ):
								for col in range(cols - 1	,			-1	,			-1 ):
												_snake_case :			Tuple  						=   dp_array[row][col + 1]
												_snake_case :			Optional[int]  						=   dp_array[row + 1][col + 1]
												_snake_case :			str  						=   dp_array[row + 1][col]

												if mat[row][col] == 1:
																_snake_case :			int  						=   1 + min(lowerCamelCase_	,			lowerCamelCase_	,			lowerCamelCase_ )
																_snake_case :			List[Any]  						=   max(dp_array[row][col]	,			lowerCamelCase_ )
												else:
																_snake_case :			Optional[int]  						=   0

				return largest_square_area

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Tuple  						=   [0] * (cols + 1)
				_snake_case :			Optional[Any]  						=   [0] * (cols + 1)
				_snake_case :			Optional[int]  						=   0
				for row in range(rows - 1	,			-1	,			-1 ):
								for col in range(cols - 1	,			-1	,			-1 ):
												_snake_case :			Union[str, Any]  						=   current_row[col + 1]
												_snake_case :			Optional[int]  						=   next_row[col + 1]
												_snake_case :			int  						=   next_row[col]

												if mat[row][col] == 1:
																_snake_case :			Union[str, Any]  						=   1 + min(lowerCamelCase_	,			lowerCamelCase_	,			lowerCamelCase_ )
																_snake_case :			str  						=   max(current_row[col]	,			lowerCamelCase_ )
												else:
																_snake_case :			Optional[Any]  						=   0
								_snake_case :			str  						=   current_row

				return largest_square_area


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))













from __future__ import annotations

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Dict  						=   list(range(len(__lowerCAmelCase ) ) )
				_snake_case :			Optional[int]  						=   [v / w for v, w in zip(__lowerCAmelCase	,			__lowerCAmelCase )]
				index.sort(key=lambda __lowerCAmelCase : ratio[i]	,			reverse=__lowerCAmelCase )

				_snake_case :			float  						=   0
				_snake_case :			list[float]  						=   [0] * len(__lowerCAmelCase )
				for i in index:
								if weight[i] <= capacity:
												_snake_case :			List[Any]  						=   1
												max_value += value[i]
												capacity -= weight[i]
								else:
												_snake_case :			Any  						=   capacity / weight[i]
												max_value += value[i] * capacity / weight[i]
												break

				return max_value, fractions


if __name__ == "__main__":
		import doctest

		doctest.testmod()






