Calculation number of islands of a particular lake, or number of enclosed inner polygon

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1

How to calculate number of islands of a particular lake according to current OSM data, like Lac Simard

Some large lakes may composed of thousands islands, so it is impossible to count one by one

2

You can’t count them directly alone. A ring may be split into multiple inner sections. I don’t know whether someone has done it for =multipolygon , but fortunately there is an example for =roundabout . Counting roundabouts

way.all(if: is_closed() == 0) -> .open;
(.all; - .open;) -> .closed;
make counter num = closed.count(ways) -> .count;
foreach.open {
  if (! lrs_in(u(id()), visited_ids.set(t['ids'])))
  {
    complete {
      node(w);
      way.open(bn);
    }
    make visited
      ids = lrs_union(set(id()), visited_ids.set(t['ids']))
      -> .visited_ids;
    .count convert counter num = t['num'] + 1 -> .count;
  }
}

I used a similar query to find such examples to verify it works overpass turbo
Relation: ‪Lac des Deux-Montagnes‬ (‪331499‬) | OpenStreetMap has 88 closed + 2 rings = 90 islands (selected role:inner closed, and manually observed from JOSM) overpass turbo
Note this can also be used to count islands for water=river