'''simple docstring'''

from manim import *



class 			UpperCAmelCase  (						a__					):





       '''simple docstring'''



       def _lowerCAmelCase(						self )  ->  Optional[int]:
        lowercase__				:    Union[str, Any]  =					Rectangle(height=0.5	,   width=0.5 )
        lowercase__				:    Optional[Any]  =					Rectangle(height=0.4_6	,   width=0.4_6 ).set_stroke(width=0 )

        lowercase__				:    Union[str, Any]  =					[mem.copy() for i in range(6 )]
        lowercase__				:    List[Any]  =					[mem.copy() for i in range(6 )]
        lowercase__				:    str  =					VGroup(*__lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0 )
        lowercase__				:    int  =					VGroup(*__lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0 )
        lowercase__				:    Dict  =					VGroup(__lowerCAmelCase	,   __lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0 )
        lowercase__				:    Dict  =					Text('''CPU'''	,   font_size=24 )
        lowercase__				:    Dict  =					Group(__lowerCAmelCase	,   __lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0.5	,   aligned_edge=__lowerCAmelCase )
        cpu.move_to([-2.5, -0.5, 0] )
        self.add(__lowerCAmelCase )

        lowercase__				:    List[Any]  =					[mem.copy() for i in range(1 )]
        lowercase__				:    List[str]  =					VGroup(*__lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0 )
        lowercase__				:    Optional[Any]  =					Text('''GPU'''	,   font_size=24 )
        lowercase__				:    Optional[int]  =					Group(__lowerCAmelCase	,   __lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0.5	,   aligned_edge=__lowerCAmelCase )
        gpu.align_to(__lowerCAmelCase	,   __lowerCAmelCase )
        gpu.set_x(gpu.get_x() - 1 )

        self.add(__lowerCAmelCase )

        lowercase__				:    str  =					[mem.copy() for i in range(6 )]
        lowercase__				:    Tuple  =					VGroup(*__lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0 )

        lowercase__				:    Any  =					Text('''Model'''	,   font_size=24 )
        lowercase__				:    Any  =					Group(__lowerCAmelCase	,   __lowerCAmelCase ).arrange(__lowerCAmelCase	,   buff=0.5	,   aligned_edge=__lowerCAmelCase )
        model.move_to([3, -1.0, 0] )

        self.play(
            Create(__lowerCAmelCase	,   run_time=1 )	,   Create(__lowerCAmelCase	,   run_time=1 )	,   Create(__lowerCAmelCase	,   run_time=1 )	,   )

        lowercase__				:    Any  =					MarkupText(
            F"""First, an empty model skeleton is loaded\ninto <span fgcolor='{YELLOW}'>memory</span> without using much RAM."""	,   font_size=24	,   )

        lowercase__				:    Tuple  =					Square(side_length=2.2 )
        key.move_to([-5, 2, 0] )

        lowercase__				:    Optional[Any]  =					MarkupText(
            F"""<b>Key:</b>\n\n<span fgcolor='{YELLOW}'>●</span> Empty Model"""	,   font_size=18	,   )

        key_text.move_to([-5, 2.4, 0] )

        step_a.move_to([2, 2, 0] )
        self.play(Write(__lowerCAmelCase	,   run_time=2.5 )	,   Write(__lowerCAmelCase )	,   Write(__lowerCAmelCase ) )

        self.add(__lowerCAmelCase )

        lowercase__				:    Tuple  =					[]
        lowercase__				:    Optional[Any]  =					[]
        lowercase__				:    Any  =					[]
        for i, rect in enumerate(__lowerCAmelCase ):
         lowercase__				:    List[str]  =					Rectangle(height=0.4_6	,   width=0.4_6 ).set_stroke(width=0.0 ).set_fill(__lowerCAmelCase	,   opacity=0.7 )
         cpu_target.move_to(__lowerCAmelCase )
         cpu_target.generate_target()
         lowercase__				:    str  =					0.4_6 / 4
         lowercase__				:    Optional[int]  =					0.4_6 / 3

         if i == 0:
          cpu_target.target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT )	,   buff=0.0_2	,   direction=__lowerCAmelCase )
          cpu_target.target.set_x(cpu_target.target.get_x() + 0.1 )
         elif i == 3:
          cpu_target.target.next_to(cpu_targs[0].target	,   direction=__lowerCAmelCase	,   buff=0.0 )
         else:
          cpu_target.target.next_to(cpu_targs[i - 1].target	,   direction=__lowerCAmelCase	,   buff=0.0 )
         cpu_targs.append(__lowerCAmelCase )

         first_animations.append(rect.animate(run_time=0.5 ).set_stroke(__lowerCAmelCase ) )
         second_animations.append(MoveToTarget(__lowerCAmelCase	,   run_time=1.5 ) )

        self.play(*__lowerCAmelCase )
        self.play(*__lowerCAmelCase )

        self.wait()


'''simple docstring'''

def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):

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

  lowercase__				:    int  =					update_area_of_max_square(UpperCAmelCase		,     col + 1     )
  lowercase__				:    Any  =					update_area_of_max_square(row + 1		,     col + 1     )
  lowercase__				:    str  =					update_area_of_max_square(row + 1		,     UpperCAmelCase     )

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

 lowercase__				:    Dict  =					[0]
 update_area_of_max_square(0		,     0     )
 return largest_square_area[0]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):

 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]

  lowercase__				:    int  =					update_area_of_max_square_using_dp_array(UpperCAmelCase		,     col + 1		,     UpperCAmelCase     )
  lowercase__				:    Optional[int]  =					update_area_of_max_square_using_dp_array(row + 1		,     col + 1		,     UpperCAmelCase     )
  lowercase__				:    Any  =					update_area_of_max_square_using_dp_array(row + 1		,     UpperCAmelCase		,     UpperCAmelCase     )

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

 lowercase__				:    Any  =					[0]
 lowercase__				:    List[Any]  =					[[-1] * cols for _ in range(UpperCAmelCase     )]
 update_area_of_max_square_using_dp_array(0		,     0		,     UpperCAmelCase     )

 return largest_square_area[0]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    Optional[int]  =					[[0] * (cols + 1) for _ in range(rows + 1     )]
 lowercase__				:    str  =					0
 for row in range(rows - 1		,     -1		,     -1     ):
  for col in range(cols - 1		,     -1		,     -1     ):
   lowercase__				:    str  =					dp_array[row][col + 1]
   lowercase__				:    Optional[Any]  =					dp_array[row + 1][col + 1]
   lowercase__				:    str  =					dp_array[row + 1][col]

   if mat[row][col] == 1:
    lowercase__				:    Dict  =					1 + min(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )
    lowercase__				:    str  =					max(dp_array[row][col]		,     UpperCAmelCase     )
   else:
    lowercase__				:    Any  =					0

 return largest_square_area
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    List[str]  =					[0] * (cols + 1)
 lowercase__				:    str  =					[0] * (cols + 1)
 lowercase__				:    Tuple  =					0
 for row in range(rows - 1		,     -1		,     -1     ):
  for col in range(cols - 1		,     -1		,     -1     ):
   lowercase__				:    List[Any]  =					current_row[col + 1]
   lowercase__				:    Any  =					next_row[col + 1]
   lowercase__				:    Optional[Any]  =					next_row[col]

   if mat[row][col] == 1:
    lowercase__				:    List[str]  =					1 + min(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )
    lowercase__				:    List[str]  =					max(current_row[col]		,     UpperCAmelCase     )
   else:
    lowercase__				:    int  =					0
  lowercase__				:    int  =					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]]))

