




'''simple docstring'''





def       __a      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       int   ,		_UpperCamelCase:       list[list[int]]       )		->					int:

     """simple docstring"""




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

          _snake_case				= update_area_of_max_square(_UpperCamelCase   ,		col + 1       )
          _snake_case				= update_area_of_max_square(row + 1   ,		col + 1       )
          _snake_case				= update_area_of_max_square(row + 1   ,		_UpperCamelCase       )

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

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





def       __a      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       int   ,		_UpperCamelCase:       list[list[int]]       )		->					int:

     """simple docstring"""




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

          _snake_case				= update_area_of_max_square_using_dp_array(_UpperCamelCase   ,		col + 1   ,		_UpperCamelCase       )
          _snake_case				= update_area_of_max_square_using_dp_array(row + 1   ,		col + 1   ,		_UpperCamelCase       )
          _snake_case				= update_area_of_max_square_using_dp_array(row + 1   ,		_UpperCamelCase   ,		_UpperCamelCase       )

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

     _snake_case				= [0]
     _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       __a      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       int   ,		_UpperCamelCase:       list[list[int]]       )		->					int:

     """simple docstring"""




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

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

     return largest_square_area





def       __a      (  _UpperCamelCase:       int   ,		_UpperCamelCase:       int   ,		_UpperCamelCase:       list[list[int]]       )		->					int:

     """simple docstring"""




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

               if mat[row][col] == 1:
                    _snake_case				= 1 + min(_UpperCamelCase   ,		_UpperCamelCase   ,		_UpperCamelCase       )
                    _snake_case				= max(current_row[col]   ,		_UpperCamelCase       )
               else:
                    _snake_case				= 0
          _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]]))








'''simple docstring'''





from __future__ import annotations

from typing import Any

class   _a							:






     def __init__(					self   ,_SCREAMING_SNAKE_CASE       )				->     None:
          _snake_case				= num_of_nodes
          _snake_case				= []
          _snake_case				= {}






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       )				->     None:
          self.m_edges.append([u_node, v_node, weight]       )






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE       )				->     int:

          if self.m_component[u_node] == u_node:
               return u_node
          return self.find_component(self.m_component[u_node]       )






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE       )				->     None:

          if self.m_component[u_node] != u_node:
               for k in self.m_component:
                    _snake_case				= self.find_component(_SCREAMING_SNAKE_CASE       )






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       )				->     None:

          if component_size[u_node] <= component_size[v_node]:
               _snake_case				= v_node
               component_size[v_node] += component_size[u_node]
               self.set_component(_SCREAMING_SNAKE_CASE       )

          elif component_size[u_node] >= component_size[v_node]:
               _snake_case				= self.find_component(_SCREAMING_SNAKE_CASE       )
               component_size[u_node] += component_size[v_node]
               self.set_component(_SCREAMING_SNAKE_CASE       )






     def 							_lowercase      (					self       )				->     None:
          _snake_case				= []
          _snake_case				= 0

          _snake_case				= [-1] * self.m_num_of_nodes

          # A list of components (initialized to all of the nodes)
          for node in range(self.m_num_of_nodes       ):
               self.m_component.update({node: node}       )
               component_size.append(1       )

          _snake_case				= self.m_num_of_nodes

          while num_of_components > 1:
               for edge in self.m_edges:
                    _snake_case				,   _snake_case				,   _snake_case				= edge

                    _snake_case				= self.m_component[u]
                    _snake_case				= self.m_component[v]

                    if u_component != v_component:

                         for component in (u_component, v_component):
                              if (
                                  minimum_weight_edge[component] == -1
                                  or minimum_weight_edge[component][2] > w
                              ):
                                   _snake_case				= [u, v, w]

               for edge in minimum_weight_edge:
                    if isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
                         _snake_case				,   _snake_case				,   _snake_case				= edge

                         _snake_case				= self.m_component[u]
                         _snake_case				= self.m_component[v]

                         if u_component != v_component:
                              mst_weight += w
                              self.union(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       )
                              print(f"""Added edge [{u} - {v}]\nAdded weight: {w}\n"""       )
                              num_of_components -= 1

               _snake_case				= [-1] * self.m_num_of_nodes
          print(f"""The total weight of the minimal spanning tree is: {mst_weight}"""       )







def       __a      (  )		->					None:

     """simple docstring"""






if __name__ == "__main__":
   import doctest

   doctest.testmod()


