How to calculate the sum of values in a tree using SQL?

If you were using Oracle DBMS that would be pretty straightforward since Oracle supports tree queries with the CONNECT BY/STARTS WITH syntax. For SQL Server I think you might find Common Table Expressions useful.

Trees don't work well with SQL. If you have very (very very) few write accesses, you could change the tree implementation to use nested sets, that would make this query incredibly easy (SELECT SUM(points) FROM users where left > x and right It's probably better to just do the recursion in you client.

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