bool
subgrid_consistency (pset_t *subgrid[grid_size])
/*
 * subgrid_consistency check if subgrid is consistent
 *
 * a subgrid is consistent if and only if :
 * _ each color appears once at least in subgrid
 * _ two singleton in subgrid are not the same
 *
 * RETURN VALUE : true if subgrid is consistent, false otherwise
 */
{
  unsigned int i;
  pset_t color_appeared, color_singleton;
  bool singleton = true;//true if each singleton in subgrid appears no more once
  color_appeared = pset_empty();
  color_singleton = pset_empty();

  for (i = 0; i < grid_size; i++)
    {
      if (pset_is_singleton(*subgrid[i]))
    {
      if (pset_is_included(*subgrid[i], color_singleton))
        {
          //subgrid[i] is a singleton ever met before
          singleton = false;
          break;
        }
      color_singleton = pset_or(color_singleton, *subgrid[i]);
    }
      color_appeared = pset_or(color_appeared, *subgrid[i]);
    }

  return pset_is_included(pset_full(grid_size), color_appeared) && singleton;
}


bool
grid_consistency (pset_t **grid)
/*
 * grid_consistency check if grid is consistency
 *
 * a grid is consistent if and only if each subgrid is consistent
 *
 * a subgrid is consistent if and only if :
 * _ each color appears once at least in subgrid
 * _ two singleton in subgrid are not the same
 *
 * RETURN VALUE : true if grid is consistent, false otherwise
 */
{
  return subgrid_map(grid, subgrid_consistency);
}