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LINQ get rows from a table that don't exist in another table when using group by?

I have two three tables books, authors and groups.

books: bookId, name, authorId....

authors: authorId, firstName, LastName....

groups: groupID, name, authorId...

i need to select all authorIds that doesn't belong to any groups and doesn't have less than 3 books published between two dates.

 List<int> authorId= new List<int>(db.Books.GroupBy(x => x.authorId)
                .Where(x => x.Any(y => y.datePublished <= now && y.datePublished >= date) && x.Count() > 2)
                .Select(x => x.FirstOrDefault().authorId)).Distinct().ToList();

Well, assuming that you're using Entity Framework and you have the proper navigation properties in your model, you can do something like this:

var authorIds= db.Authors
                 .Where(a=>a.Books.Count(y => y.datePublished <= now && y.datePublished >= date)>2 && !a.Groups.Any())
                 .ToList();

Another solution that came to my mind now but I'm not sure if it works is using two group joins :

var authorId=(from a in db.Authors
              join b in db.Books on a.authorId equals b.authorId into g1
              join g in db.Groups on a.authorId equals g.authorId into g2
              where  g1.Count(y => y.datePublished <= now && y.datePublished >= date)>0 && !g2.Any()
              select a.authorId).ToList();

But I definitely prefer my first solution, it's more readable and easy too.

I guess this would work:

List<int> authorId = (List<int>)db.Books
    .Where(x => x.datePublished >= InitialDate)
    .Where(x => x.datePublished <= FinalDate)
    .GroupBy(x => x.authorId)
    .Select(g => new { authorId = g.Key, count = g.Count() })
    .Where(g => g.Count >= 3)
    .Select(g.authorId);

I make every single step so you can see it better, fell free to optimized as needed. The key thing here is the new { authorId = g.Key, count = g.Count() } .

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