





'''simple docstring'''






from __future__ import annotations




class  UpperCAmelCase     :




      def __init__(			self			: Dict			,			__snake_case			: int  )				->      Tuple:
            _lowerCAmelCase							     =							order

            # a_{0} ... a_{k}
            _lowerCAmelCase							     =							[1.0] + [0.0] * order
            # b_{0} ... b_{k}
            _lowerCAmelCase							     =							[1.0] + [0.0] * order

            # x[n-1] ... x[n-k]
            _lowerCAmelCase							     =							[0.0] * self.order
            # y[n-1] ... y[n-k]
            _lowerCAmelCase							     =							[0.0] * self.order




      def 				lowercase__    (			self			: Optional[int]			,			__snake_case			: list[float]			,			__snake_case			: list[float]  )				->      Any:
            if len(UpperCAmelCase_  ) < self.order:
                  _lowerCAmelCase							     =							[1.0, *a_coeffs]

            if len(UpperCAmelCase_  ) != self.order + 1:
                  _lowerCAmelCase							     =							(
                      f"Expected a_coeffs to have {self.order + 1} elements "
                      f"for {self.order}-order filter, got {len(UpperCAmelCase_  )}"
                  )
                  raise ValueError(UpperCAmelCase_  )

            if len(UpperCAmelCase_  ) != self.order + 1:
                  _lowerCAmelCase							     =							(
                      f"Expected b_coeffs to have {self.order + 1} elements "
                      f"for {self.order}-order filter, got {len(UpperCAmelCase_  )}"
                  )
                  raise ValueError(UpperCAmelCase_  )

            _lowerCAmelCase							     =							a_coeffs
            _lowerCAmelCase							     =							b_coeffs




      def 				lowercase__    (			self			: Dict			,			__snake_case			: float  )				->      Optional[int]:
            _lowerCAmelCase							     =							0.0

            # Start at index 1 and do index 0 at the end.
            for i in range(1			,			self.order + 1  ):
                  result += (
                      self.b_coeffs[i] * self.input_history[i - 1]
                      - self.a_coeffs[i] * self.output_history[i - 1]
                  )

            _lowerCAmelCase							     =							(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

            _lowerCAmelCase							     =							self.input_history[:-1]
            _lowerCAmelCase							     =							self.output_history[:-1]

            _lowerCAmelCase							     =							sample
            _lowerCAmelCase							     =							result

            return result








def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(UpperCamelCase_	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	UpperCamelCase_		)

										if mat[row][col]:
															SCREAMING_SNAKE_CASE__													= 1 + min([right, diagonal, down]		)
															SCREAMING_SNAKE_CASE__													= max(largest_square_area[0]	,	UpperCamelCase_		)
															return sub_problem_sol
										else:
															return 0

					SCREAMING_SNAKE_CASE__													= [0]
					update_area_of_max_square(0	,	0		)
					return largest_square_area[0]






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(UpperCamelCase_	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	UpperCamelCase_	,	UpperCamelCase_		)

										if mat[row][col]:
															SCREAMING_SNAKE_CASE__													= 1 + min([right, diagonal, down]		)
															SCREAMING_SNAKE_CASE__													= max(largest_square_area[0]	,	UpperCamelCase_		)
															SCREAMING_SNAKE_CASE__													= sub_problem_sol
															return sub_problem_sol
										else:
															return 0

					SCREAMING_SNAKE_CASE__													= [0]
					SCREAMING_SNAKE_CASE__													= [[-1] * cols for _ in range(UpperCamelCase_		)]
					update_area_of_max_square_using_dp_array(0	,	0	,	UpperCamelCase_		)

					return largest_square_area[0]






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					SCREAMING_SNAKE_CASE__													= [[0] * (cols + 1) for _ in range(rows + 1		)]
					SCREAMING_SNAKE_CASE__													= 0
					for row in range(rows - 1	,	-1	,	-1		):
										for col in range(cols - 1	,	-1	,	-1		):
															SCREAMING_SNAKE_CASE__													= dp_array[row][col + 1]
															SCREAMING_SNAKE_CASE__													= dp_array[row + 1][col + 1]
															SCREAMING_SNAKE_CASE__													= dp_array[row + 1][col]

															if mat[row][col] == 1:
																				SCREAMING_SNAKE_CASE__													= 1 + min(UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)
																				SCREAMING_SNAKE_CASE__													= max(dp_array[row][col]	,	UpperCamelCase_		)
															else:
																				SCREAMING_SNAKE_CASE__													= 0

					return largest_square_area






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					SCREAMING_SNAKE_CASE__													= [0] * (cols + 1)
					SCREAMING_SNAKE_CASE__													= [0] * (cols + 1)
					SCREAMING_SNAKE_CASE__													= 0
					for row in range(rows - 1	,	-1	,	-1		):
										for col in range(cols - 1	,	-1	,	-1		):
															SCREAMING_SNAKE_CASE__													= current_row[col + 1]
															SCREAMING_SNAKE_CASE__													= next_row[col + 1]
															SCREAMING_SNAKE_CASE__													= next_row[col]

															if mat[row][col] == 1:
																				SCREAMING_SNAKE_CASE__													= 1 + min(UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)
																				SCREAMING_SNAKE_CASE__													= max(current_row[col]	,	UpperCamelCase_		)
															else:
																				SCREAMING_SNAKE_CASE__													= 0
										SCREAMING_SNAKE_CASE__													= 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]]))





