How to select path from nested sets excluding subtrees - sql

Question

I have an SQLite database, which contains trees with red and black nodes (not red-black trees though). Trees are stored as nested sets (https://en.wikipedia.org/wiki/Nested_set_model)
Name TreeId Left Right IsBlack
A 1 1 8 1
B 1 2 7 0
C 1 3 6 1
D 1 4 5 1
A 2 1 10 1
B 2 2 5 0
C 2 6 9 1
D 2 3 4 1
D 2 7 8 1
Both B and C nodes with TreeId = 2 point to D node. So D is written twice.
These trees may contain only black or only red nodes
I would like to select all paths for the specified node, that do not contain red nodes, i. e. exclude red nodes and all their subtrees from result
Examples:
For record:
Name TreeId Left Right IsBlack
A 1 1 8 1
the result will be:
Name TreeId Left Right IsBlack
A 1 1 8 1
For record:
Name TreeId Left Right IsBlack
C 1 3 6 1
the result will be:
Name TreeId Left Right IsBlack
C 1 3 6 1
D 1 4 5 1
And, finally, for record:
Name TreeId Left Right IsBlack
A 2 1 10 1
The result will be:
Name TreeId Left Right IsBlack
A 2 1 10 1
C 2 6 9 1
D 2 7 8 1
To keep it simple, let's assume that there is another query, which selects TreeId, Left and Right parameters of the searched node by its name.
So I came up with the following query (for node A):
SELECT Nodes.* FROM Nodes
LEFT JOIN Nodes as n ON Nodes.[TreeId] = n.TreeId AND n.IsBlack = 0 AND Nodes.Left >= n.Left AND Nodes.Right <= n.Right
AND n.Left >= 1 AND n.Right <= 10
WHERE Nodes.TreeId = 2 AND Nodes.Left >= 1 AND Nodes.[Right] <= 10 AND n.Name IS NULL
The query seems to work, but it's terribly slow because of left join even with indexes.
So I was wondering, is there a way to optimize the query in terms of SQLite avoiding left join (for example using inner joins, unions, etc)
P.S. I cannot change the way the data is stored, but I can modify database schema (add new fields).
P.P.S. I understand, that I can query all results, and then filter them on the code side. The other option is to store two types of trees in db: one with red and black nodes, and the other one with black nodes only. However, both of these solutions are last resorts.
Thanks in advance

Answer 1

Okay, I don't know if it'll be faster or not - can't tell with only a few rows of data, but this one uses a recursive CTE to at least get the same results as your examples:
WITH RECURSIVE n AS
(SELECT * FROM nodes WHERE name= ?1 AND treeid = ?2 AND isblack = 1
UNION ALL
SELECT n2.name, n2.treeid, n2.left, n2.right, n2.isblack
FROM n
JOIN nodes AS n2
ON n2.treeid = n.treeid
AND (n2.left = n.left + 1 OR n2.right = n.right - 1)
WHERE n2.isblack = 1)
SELECT * FROM n ORDER BY name
You'll probably want an index on nodes(isblack, treeid, name) (And don't forget to run a PRAGMA optimize once in a while.) Bind/replace ?1 and ?2 with the obvious values for a particular run of the query.