How to efficiently find minimum associated ID after applying transitivity - sql-server

Question

I've a very large table with ID variables in two columns. I'd like to find the minimum associated ID after applying transitivity. For example, if ID1 = 1 and ID2 = 2 for one record and ID1 = 2 and ID2 = 3 for another record, I'd like the results to ultimately yield three records where the first column has an ID (1, 2, and 3) and the second column has a Min_ID (all equal to 1, in the above example).
I've determined that at most there are 6 ways IDs can be related, and I believe the below is a minimum functioning example.
Is there a more efficient way to do this?
Source
| ID1 | ID2 |
|------|-------|
| 1 | 1 |
| 2 | 2 |
| 1 | 1 |
| 1 | 2 |
| 2 | 11 |
| 11 | 13 |
| 13 | 99 |
| 99 | 1000 |
| 1000 | 97887 |
| 3 | 5 |
| 5 | 17 |
| 17 | 19 |
| 23 | 34 |
Results
| ID | Min_ID |
|-------|--------|
| 1 | 1 |
| 2 | 1 |
| 3 | 3 |
| 5 | 3 |
| 11 | 1 |
| 13 | 1 |
| 17 | 3 |
| 19 | 3 |
| 23 | 23 |
| 34 | 23 |
| 99 | 1 |
| 1000 | 1 |
| 97887 | 1 |
Functioning albeit potentially-inefficient working example:
IF OBJECT_ID('tempdb..##IDs') IS NOT NULL DROP TABLE ##IDs
GO
CREATE TABLE ##IDs
(
ID1 int
,ID2 int
);
INSERT INTO ##IDs (ID1, ID2)
VALUES
(1, 1),
(2, 2),
(1, 1),
(1, 2),
(2, 11),
(11, 13),
(13, 99),
(99, 1000),
(1000, 97887),
(3, 5),
(5, 17),
(17, 19),
(23, 34)
;
WITH t1 AS
(
SELECT
ID1
,ID2
FROM ##IDs
UNION
SELECT
ID2
,ID1
FROM ##IDs
),
t2 AS
(
SELECT
*
FROM t1
UNION
SELECT
a.ID1
,b.ID2
FROM t1 a
LEFT JOIN t1 b ON
a.ID2 = b.ID1
UNION
SELECT
b.ID2
,a.ID1
FROM t1 a
LEFT JOIN t1 b ON
a.ID2 = b.ID1
),
t3 AS
(
SELECT
*
FROM t2
UNION
SELECT
a.ID1
,b.ID2
FROM t2 a
LEFT JOIN t2 b ON
a.ID2 = b.ID1
UNION
SELECT
b.ID2
,a.ID1
FROM t2 a
LEFT JOIN t2 b ON
a.ID2 = b.ID1
),
t4 AS
(
SELECT
*
FROM t3
UNION
SELECT
a.ID1
,b.ID2
FROM t3 a
LEFT JOIN t3 b ON
a.ID2 = b.ID1
UNION
SELECT
b.ID2
,a.ID1
FROM t3 a
LEFT JOIN t3 b ON
a.ID2 = b.ID1
)
SELECT
ID1 AS [ID]
,MIN(ID2) Min_ID
FROM t4
GROUP BY
ID1

Answer 1

The complexity here for me was finding an appropriate stopping condition for the linking recursion. That said, it's really quite simple: stop linking when the ID links to itself.
IF OBJECT_ID('tempdb..##IDs') IS NOT NULL DROP TABLE ##IDs
GO
CREATE TABLE ##IDs
(
ID1 int
,ID2 int
);
INSERT INTO ##IDs (ID1, ID2)
VALUES
(1, 1),
(2, 2),
(1, 1),
(1, 2),
(2, 11),
(11, 13),
(13, 99),
(99, 1000),
(1000, 97887),
(3, 5),
(5, 17),
(17, 19),
(23, 34)
;
WITH t1 AS
(
SELECT
ID1
,ID2
FROM ##IDs
UNION
SELECT
ID2
,ID1
FROM ##IDs
UNION ALL
SELECT
c.ID1
,t1.ID2
FROM ##IDs c
INNER JOIN t1 ON
c.ID2 = t1.ID1
WHERE
c.ID1 <> c.ID2
UNION ALL
SELECT
t1.ID2
,c.ID1
FROM ##IDs c
INNER JOIN t1 ON
c.ID2 = t1.ID1
WHERE
c.ID1 <> c.ID2
)
SELECT
ID1 AS [ID]
,MIN(ID2) Min_ID
FROM t1
GROUP BY
ID1
;