





def      lowerCAmelCase_ (       __a	,    __a	,    __a		)     ->		int:







  """simple docstring"""





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

    lowerCamelCase__:      Union[str, Any]			  =update_area_of_max_square(__a	,    col + 1		)
    lowerCamelCase__:      Dict			  =update_area_of_max_square(row + 1	,    col + 1		)
    lowerCamelCase__:      List[str]			  =update_area_of_max_square(row + 1	,    __a		)

    if mat[row][col]:
      lowerCamelCase__:      Tuple			  =1 + min([right, diagonal, down]		)
      lowerCamelCase__:      str			  =max(largest_square_area[0]	,    __a		)
      return sub_problem_sol
    else:
      return 0

  lowerCamelCase__:      Dict			  =[0]
  update_area_of_max_square(0	,    0		)
  return largest_square_area[0]





def      lowerCAmelCase_ (       __a	,    __a	,    __a		)     ->		int:







  """simple docstring"""





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

    lowerCamelCase__:      str			  =update_area_of_max_square_using_dp_array(__a	,    col + 1	,    __a		)
    lowerCamelCase__:      str			  =update_area_of_max_square_using_dp_array(row + 1	,    col + 1	,    __a		)
    lowerCamelCase__:      Dict			  =update_area_of_max_square_using_dp_array(row + 1	,    __a	,    __a		)

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

  lowerCamelCase__:      Union[str, Any]			  =[0]
  lowerCamelCase__:      Optional[int]			  =[[-1] * cols for _ in range(__a		)]
  update_area_of_max_square_using_dp_array(0	,    0	,    __a		)

  return largest_square_area[0]





def      lowerCAmelCase_ (       __a	,    __a	,    __a		)     ->		int:







  """simple docstring"""





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

      if mat[row][col] == 1:
        lowerCamelCase__:      str			  =1 + min(__a	,    __a	,    __a		)
        lowerCamelCase__:      Tuple			  =max(dp_array[row][col]	,    __a		)
      else:
        lowerCamelCase__:      Tuple			  =0

  return largest_square_area





def      lowerCAmelCase_ (       __a	,    __a	,    __a		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      Union[str, Any]			  =[0] * (cols + 1)
  lowerCamelCase__:      Dict			  =[0] * (cols + 1)
  lowerCamelCase__:      List[Any]			  =0
  for row in range(rows - 1	,    -1	,    -1		):
    for col in range(cols - 1	,    -1	,    -1		):
      lowerCamelCase__:      Optional[int]			  =current_row[col + 1]
      lowerCamelCase__:      int			  =next_row[col + 1]
      lowerCamelCase__:      Optional[int]			  =next_row[col]

      if mat[row][col] == 1:
        lowerCamelCase__:      Dict			  =1 + min(__a	,    __a	,    __a		)
        lowerCamelCase__:      Dict			  =max(current_row[col]	,    __a		)
      else:
        lowerCamelCase__:      Tuple			  =0
    lowerCamelCase__:      List[Any]			  =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 collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def      lowerCAmelCase_ (       )     ->		Optional[int]:







  """simple docstring"""





  lowerCamelCase__  ,					lowerCamelCase__:      int			  =9, 14  # noqa: F841
  lowerCamelCase__:      List[Any]			  =[
      [0, 1, 4],
      [0, 7, 8],
      [1, 2, 8],
      [7, 8, 7],
      [7, 6, 1],
      [2, 8, 2],
      [8, 6, 6],
      [2, 3, 7],
      [2, 5, 4],
      [6, 5, 2],
      [3, 5, 14],
      [3, 4, 9],
      [5, 4, 10],
      [1, 7, 11],
  ]

  lowerCamelCase__:      List[str]			  =defaultdict(__a		)
  for nodea, nodea, cost in edges:
    adjancency[nodea].append([nodea, cost]		)
    adjancency[nodea].append([nodea, cost]		)

  lowerCamelCase__:      List[str]			  =mst(__a		)

  lowerCamelCase__:      Union[str, Any]			  =[
      [7, 6, 1],
      [2, 8, 2],
      [6, 5, 2],
      [0, 1, 4],
      [2, 5, 4],
      [2, 3, 7],
      [0, 7, 8],
      [3, 4, 9],
  ]

  for answer in expected:
    lowerCamelCase__:      Optional[int]			  =tuple(answer[:2]		)
    lowerCamelCase__:      List[Any]			  =tuple(edge[::-1]		)
    assert edge in result or reverse in result

