static choice_t *
stack_push(choice_t *stack, pset_t **grid)
{
  unsigned int i, j;
  unsigned int i_choice, j_choice;
  unsigned int min_card = grid_size+1;
  char str[grid_size];
  char str_choice[grid_size];

  choice_t *new_element = malloc(sizeof (choice_t));
  if (new_element == NULL)
    {
      fprintf(output_file, "error : Out of memory!\n");
    }

  new_element->grid = grid_copy(grid);

  // getting the minimal cardinality
  for (i = 0; i < grid_size; i++)
    {
      for (j = 0; j < grid_size; j++)
    {
      if (pset_cardinality(grid[i][j]) < min_card
          && (!pset_is_singleton(grid[i][j])) )
        {
          min_card = pset_cardinality(grid[i][j]);
          i_choice = i;
          j_choice = j;
        }
    }
    }


  pset2str(str, grid[i_choice][j_choice]);
  pset2str(str_choice, pset_leftmost(grid[i_choice][j_choice]));
  fprintf(output_file, "Cell : grid[%d][%d] = '%s', "
      "choice = '%s' \n ", i_choice, j_choice, str, str_choice);
  new_element->x = i_choice;
  new_element->y = j_choice;
  new_element->choice = pset_leftmost(grid[i_choice][j_choice]);
  new_element->grid[i_choice][j_choice] =
    pset_leftmost(grid[i_choice][j_choice]);


  if (!grid_consistency(new_element->grid) )
    {
      return NULL;
    }
  new_element->previous = stack;

  return new_element;

}