How to create post-order traversal in SQL? - sql

Question

Having a tree structure in database (id, parentId, order) where order means some value to sort per parent (it means order in parent list), how one can build full-SQL query to traverse this table in POST-ORDER?
What is post order is described on wiki, though only for binary trees - https://en.wikipedia.org/wiki/Tree_traversal
Not all of them is applyable to custom tree (for example IN-ORDER), but POST-ORDER is actully applyable:
A
/ \
B C
/|\
D E F
output will be:
B D E F C A
The same in SQL data table:
|Id |ParentId | Order
|___|_________|______
|A |null |0
|B |A |0
|C |A |1
|D |C |0
|E |C |1
|F |C |2
I have been struggling with it quite a time, but looks like CTE doesn't allow inner ORDER BY clause (omg, why?!), so this task becomes impossible at my current level without stored procedures.

Answer 1

More as a proof of concept than a usable answer, here's a CTE-based version. It uses STRING_AGG to concatenate the children of each node in order, then recursively replaces each node with its children to build the output string - this means it wouldn't work in situations where node keys are substrings of one another.
DECLARE #t TABLE
(id CHAR(1) NOT NULL PRIMARY KEY,
parentid CHAR(1) NULL,
roworder TINYINT NOT NULL
)
INSERT #t (id, parentid, roworder)
VALUES('A', NULL, 0),
('B','A',0),
('C','A',1),
('D','C',0),
('E','C',1),
('F','C',2),
('G','E',0),-- two extra nodes to prove that this isn't a one-off
('H','E',1)
;WITH aggCTE
AS
(
SELECT parentid, STRING_AGG(CONVERT(VARCHAR(MAX), id), ' ') WITHIN GROUP (ORDER BY Roworder) AS children
FROM #t
GROUP BY parentid
)
,recCTE
AS
(
SELECT a.parentid,
a.children,
CAST(ISNULL(a.parentid,'') AS VARCHAR(MAX)) AS processed, --to prevent loops
0 AS seq, --to pick the right output row
a.children AS firstnode --to disambiguate if the data contains multiple trees
FROM aggCTE AS a
WHERE a.parentid IS NULL
UNION ALL
SELECT a.parentid,
REPLACE(a.children, b.parentid, CONCAT(b.children, ' ', b.parentid)) AS children,
CONCAT(a.processed, b.parentid) AS processed,
a.seq + 1 AS seq,
a.firstnode
FROM recCTE AS a
JOIN aggCTE AS b
ON CHARINDEX(b.parentid, a.children) > 0
AND CHARINDEX(b.parentid, a.processed) = 0
)
,rnCTE
AS
(
SELECT children,
ROW_NUMBER() OVER (PARTITION BY firstnode ORDER BY seq DESC) AS rn
FROM recCTE
)
SELECT children AS post_order_traversal
FROM rnCTE
WHERE rn = 1

Answer 2

Found solution by simply implementing it as is:
If(OBJECT_ID('tempdb..#result') Is Not Null) Drop Table #result;
If(OBJECT_ID('tempdb..#stack') Is Not Null) Drop Table #stack;
create table #result (id int not null identity primary key, [value] bigint null);
create table #stack (id int not null identity primary key, [value] bigint null);
INSERT INTO #stack values(null) --inserting root identifiers here
WHILE EXISTS (SELECT * FROM #stack)
BEGIN
declare #stack_id int, #stack_value bigint
select top 1 #stack_id=id, #stack_value=value from #stack order by id desc
delete from #stack where id=#stack_id
INSERT INTO #stack
-- here comes our query, which should fetch children of specified id and order it
select tos.id
from inputTable as t
where (ISNULL(#stack_value, 0) = 0 AND t.ParentId IS NULL) OR (ISNULL(#stack_value, 0) != 0 AND t.ParentId = #stack_value)
order by t.[order] asc
insert into #result values(#stack_value)
END
select [value] from #result order by id desc
If(OBJECT_ID('tempdb..#result') Is Not Null) Drop Table #result;
If(OBJECT_ID('tempdb..#stack') Is Not Null) Drop Table #stack;
As of now, it seems impossible with usage of CTE.