

"""simple docstring"""


def        _lowercase    (			__lowerCAmelCase     ,    __lowerCAmelCase     ,    __lowerCAmelCase							)				-> int:

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

            SCREAMING_SNAKE_CASE__      :					Any											=		update_area_of_max_square(__UpperCAmelCase     ,    col + 1							)
            SCREAMING_SNAKE_CASE__      :					List[str]											=		update_area_of_max_square(row + 1     ,    col + 1							)
            SCREAMING_SNAKE_CASE__      :					Tuple											=		update_area_of_max_square(row + 1     ,    __UpperCAmelCase							)

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

      SCREAMING_SNAKE_CASE__      :					Optional[Any]											=		[0]
      update_area_of_max_square(0     ,    0							)
      return largest_square_area[0]




def        _lowercase    (			__lowerCAmelCase     ,    __lowerCAmelCase     ,    __lowerCAmelCase							)				-> int:

      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]

            SCREAMING_SNAKE_CASE__      :					List[str]											=		update_area_of_max_square_using_dp_array(__UpperCAmelCase     ,    col + 1     ,    __UpperCAmelCase							)
            SCREAMING_SNAKE_CASE__      :					Any											=		update_area_of_max_square_using_dp_array(row + 1     ,    col + 1     ,    __UpperCAmelCase							)
            SCREAMING_SNAKE_CASE__      :					Dict											=		update_area_of_max_square_using_dp_array(row + 1     ,    __UpperCAmelCase     ,    __UpperCAmelCase							)

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

      SCREAMING_SNAKE_CASE__      :					Any											=		[0]
      SCREAMING_SNAKE_CASE__      :					Optional[int]											=		[[-1] * cols for _ in range(__UpperCAmelCase							)]
      update_area_of_max_square_using_dp_array(0     ,    0     ,    __UpperCAmelCase							)

      return largest_square_area[0]




def        _lowercase    (			__lowerCAmelCase     ,    __lowerCAmelCase     ,    __lowerCAmelCase							)				-> int:
      SCREAMING_SNAKE_CASE__      :					List[Any]											=		[[0] * (cols + 1) for _ in range(rows + 1							)]
      SCREAMING_SNAKE_CASE__      :					Dict											=		0
      for row in range(rows - 1     ,    -1     ,    -1							):
            for col in range(cols - 1     ,    -1     ,    -1							):
                  SCREAMING_SNAKE_CASE__      :					Dict											=		dp_array[row][col + 1]
                  SCREAMING_SNAKE_CASE__      :					Dict											=		dp_array[row + 1][col + 1]
                  SCREAMING_SNAKE_CASE__      :					Optional[int]											=		dp_array[row + 1][col]

                  if mat[row][col] == 1:
                        SCREAMING_SNAKE_CASE__      :					Dict											=		1 + min(__UpperCAmelCase     ,    __UpperCAmelCase     ,    __UpperCAmelCase							)
                        SCREAMING_SNAKE_CASE__      :					Optional[int]											=		max(dp_array[row][col]     ,    __UpperCAmelCase							)
                  else:
                        SCREAMING_SNAKE_CASE__      :					str											=		0

      return largest_square_area




def        _lowercase    (			__lowerCAmelCase     ,    __lowerCAmelCase     ,    __lowerCAmelCase							)				-> int:
      SCREAMING_SNAKE_CASE__      :					Any											=		[0] * (cols + 1)
      SCREAMING_SNAKE_CASE__      :					Union[str, Any]											=		[0] * (cols + 1)
      SCREAMING_SNAKE_CASE__      :					Dict											=		0
      for row in range(rows - 1     ,    -1     ,    -1							):
            for col in range(cols - 1     ,    -1     ,    -1							):
                  SCREAMING_SNAKE_CASE__      :					List[Any]											=		current_row[col + 1]
                  SCREAMING_SNAKE_CASE__      :					List[Any]											=		next_row[col + 1]
                  SCREAMING_SNAKE_CASE__      :					Tuple											=		next_row[col]

                  if mat[row][col] == 1:
                        SCREAMING_SNAKE_CASE__      :					Any											=		1 + min(__UpperCAmelCase     ,    __UpperCAmelCase     ,    __UpperCAmelCase							)
                        SCREAMING_SNAKE_CASE__      :					List[Any]											=		max(current_row[col]     ,    __UpperCAmelCase							)
                  else:
                        SCREAMING_SNAKE_CASE__      :					List[Any]											=		0
            SCREAMING_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 sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def 		lowerCAmelCase_    (  __UpperCAmelCase:			str		,   __UpperCAmelCase:			complex		,   __UpperCAmelCase:			str = "x"		,   __UpperCAmelCase:			float = 10**-10		,   __UpperCAmelCase:			int = 1		,   )      ->	complex:
    UpperCamelCase__							:				Optional[int]          =      symbols(__UpperCAmelCase      )
    UpperCamelCase__							:				Dict          =      lambdify(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				List[str]          =      lambdify(__UpperCAmelCase		,   diff(__UpperCAmelCase		,   __UpperCAmelCase      )      )

    UpperCamelCase__							:				int          =      starting_point

    while True:
        if diff_function(__UpperCAmelCase      ) != 0:
            UpperCamelCase__							:				Optional[int]          =      prev_guess - multiplicity * func(__UpperCAmelCase      ) / diff_function(
                __UpperCAmelCase      )
        else:
            raise ZeroDivisionError('''Could not find root'''      ) from None

        # Precision is checked by comparing the difference of consecutive guesses
        if abs(next_guess - prev_guess      ) < precision:
            return next_guess

        UpperCamelCase__							:				Tuple          =      next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(F'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')

  # Find root of polynomial
  # Find fourth Root of 5
  print(F'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}''')

  # Find value of e
  print(
      'The root of log(y) - 1 = 0 is ',
      F'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
  )

  # Exponential Roots
  print(
      'The root of exp(x) - 1 = 0 is',
      F'''{newton_raphson("exp(x) - 1", 10, precision=0.005)}''',
  )

  # Find root of cos(x)
  print(F'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')

