How to rewrite slow CTE construction to match speed of temp tables

Question

I think the general advice of this community is to avoid temp tables in favor of CTEs. However, I sometimes encounter situations in which CTE constructions are very slow, while their temp table equivalents are very fast.

For example, this spins for hours and never seems to yield results. The query plan is full of nested loops.

CREATE TABLE #TRIANGLES
(
    NODE_A VARCHAR(22),
    NODE_B VARCHAR(22),
    NODE_C VARCHAR(22)
)
;


INSERT INTO #TRIANGLES VALUES
/*  150,000 ROWS  */
;


CREATE NONCLUSTERED INDEX IDX_A ON #TRIANGLES (NODE_A);

CREATE NONCLUSTERED INDEX IDX_B ON #TRIANGLES (NODE_B);

CREATE NONCLUSTERED INDEX IDX_C ON #TRIANGLES (NODE_C);



WITH
TRIANGLES_FILTERED AS
(
    -- **** FILTERING OF THE TRIANGLE TABLE OCCURS IN A CTE ****
    SELECT   *
    FROM     #TRIANGLES AS T
    WHERE    LEN(T.NODE_A) = 2  AND
             LEN(T.NODE_B) = 2  AND
             LEN(T.NODE_C) = 2
),
CONNECTABLE_NODES AS
(
    SELECT   DISTINCT T1.NODE_C AS [NODE]
    FROM     TRIANGLES_FILTERED AS T1

             INNER JOIN
             TRIANGLES_FILTERED AS T2
             ON T1.NODE_B = T2.NODE_A  AND
                T1.NODE_C = T2.NODE_B

             INNER JOIN
             TRIANGLES_FILTERED AS T3
             ON T2.NODE_B = T3.NODE_A  AND
                T2.NODE_C = T3.NODE_B

    WHERE    T1.NODE_A <> T2.NODE_C  AND
             T1.NODE_A <> T3.NODE_C  AND
             T2.NODE_A <> T3.NODE_C
)
SELECT   *
FROM     #TRIANGLES AS T1
WHERE    T1.NODE_A IN (SELECT * FROM CONNECTABLE_NODES)  AND
         T1.NODE_B IN (SELECT * FROM CONNECTABLE_NODES)  AND
         T1.NODE_C IN (SELECT * FROM CONNECTABLE_NODES)
;

Query plan: https://www.brentozar.com/pastetheplan/?id=rk_5TaiiP

Whereas, the query plan for this uses hash matches and it runs in a flash:

CREATE TABLE #TRIANGLES
(
    NODE_A VARCHAR(22),
    NODE_B VARCHAR(22),
    NODE_C VARCHAR(22)
)
;


INSERT INTO #TRIANGLES VALUES
/*  150,000 ROWS  */
;


CREATE NONCLUSTERED INDEX IDX_A ON #TRIANGLES (NODE_A);

CREATE NONCLUSTERED INDEX IDX_B ON #TRIANGLES (NODE_B);

CREATE NONCLUSTERED INDEX IDX_C ON #TRIANGLES (NODE_C);



-- **** FILTERING OF THE TRIANGLE TABLE SAVED INTO A TEMP TABLE ****
SELECT   *
INTO     #TRIANGLES_FILTERED
FROM     #TRIANGLES AS T
WHERE    LEN(T.NODE_A) = 2  AND
         LEN(T.NODE_B) = 2  AND
         LEN(T.NODE_C) = 2
;    

CREATE NONCLUSTERED INDEX IDX_A ON #TRIANGLES_FILTERED (NODE_A);

CREATE NONCLUSTERED INDEX IDX_B ON #TRIANGLES_FILTERED (NODE_B);

CREATE NONCLUSTERED INDEX IDX_C ON #TRIANGLES_FILTERED (NODE_C);



WITH
CONNECTABLE_NODES AS
(
    SELECT   DISTINCT T1.NODE_C AS [NODE]
    FROM     #TRIANGLES_FILTERED AS T1

             INNER JOIN
             #TRIANGLES_FILTERED AS T2
             ON T1.NODE_B = T2.NODE_A  AND
                T1.NODE_C = T2.NODE_B

             INNER JOIN
             #TRIANGLES_FILTERED AS T3
             ON T2.NODE_B = T3.NODE_A  AND
                T2.NODE_C = T3.NODE_B

    WHERE    T1.NODE_A <> T2.NODE_C  AND
             T1.NODE_A <> T3.NODE_C  AND
             T2.NODE_A <> T3.NODE_C
)
SELECT   *
FROM     #TRIANGLES AS T1
WHERE    T1.NODE_A IN (SELECT * FROM CONNECTABLE_NODES)  AND
         T1.NODE_B IN (SELECT * FROM CONNECTABLE_NODES)  AND
         T1.NODE_C IN (SELECT * FROM CONNECTABLE_NODES)
;

Query plan: https://www.brentozar.com/pastetheplan/?id=B1cZC6isD

How would I rewrite the first one to be as fast as a second one?

BTW, if you're wondering what all the geometry/topology is about, I needed to know how all the triangles connect with each other in the creation of this puzzle:
https://puzzling.stackexchange.com/questions/105275/dragon-summoning-spell

Answer 1

Sometimes CTE has got the wrong estimation. The temp table is good at it.

So, the CTE uses those indexes because they think fewer rows are there. The reason for the slowness of the first one is RID Lookup. If you drop your indexes or add your output column as include on your index. It will faster.

There is an awesome blog post here.

I think there is no win between them. You should use them to depends on the situation. And try them both in the same situation. In this way you can see the costs.