Ttgjyuk

I have to following input:

 id | value 
----+-------
 1 | 136
 2 | NULL
 3 | 650
 4 | NULL
 5 | NULL
 6 | NULL
 7 | 954
 8 | NULL
 9 | 104
 10 | NULL

I expect the following result:

 id | value 
----+-------
 1 | 136
 2 | 136
 3 | 650
 4 | 650
 5 | 650
 6 | 650
 7 | 954
 8 | 954
 9 | 104
 10 | 104

The trivial solution would be join the tables with a < relation, and then selecting the MAX value in a GROUP BY:

WITH tmp AS (
 SELECT t2.id, MAX(t1.id) AS lastKnownId
 FROM t t1, t t2
 WHERE
 t1.value IS NOT NULL
 AND
 t2.id >= t1.id
 GROUP BY t2.id
)
SELECT
 tmp.id, t.value
FROM t, tmp
WHERE t.id = tmp.lastKnownId;

However, the trivial execution of this code would create internally the square of the count of the rows of the input table ( O(n^2) ). I expected t-sql to optimize it out - on a block/record level, the task to do is very easy and linear, essentially a for loop ( O(n) ).

However, on my experiments, the latest MS SQL 2016 can't optimize this query correctly, making this query impossible to execute for a large input table.

Furthermore, the query has to run quickly, making a similarly easy (but very different) cursor-based solution infeasible.

Using some memory-backed temporary table could be a good compromise, but I am not sure if it can be run significantly quicker, considered that my example query using subqueries didn't work.

I am also thinking on to dig out some windowing function from the t-sql docs, what could be tricked to do what I want. For example, cumulative sum is doing some very similar, but I couldn't trick it to give the latest non-null element, and not the sum of the elements before.

The ideal solution would be a quick query without procedural code or temporary tables. Alternatively, also a solution with temporary tables is okay, but iterating the table procedurally is not.

I expected t-sql to optimize it out - on a block/record level, the
task to do is very easy and linear, essentially a for loop ( O(n) ).

That's not the query that you wrote. It may not be equivalent to the query that you wrote depending on some otherwise minor detail of the table schema. You're expecting too much from the query optimizer.

With the right indexing you can get the algorithm that you seek through the following T-SQL:

SELECT t1.id, ca.[VALUE] 
FROM dbo.[BIG_TABLE(FOR_U)] t1
CROSS APPLY (
 SELECT TOP (1) [VALUE]
 FROM dbo.[BIG_TABLE(FOR_U)] t2
 WHERE t2.ID <= t1.ID AND t2.[VALUE] IS NOT NULL
 ORDER BY t2.ID DESC
) ca; --ORDER BY t1.ID ASC

For each row, the query processor traverses the index backwards and stops when it finds a row with a non null value for [VALUE]. On my machine this finishes in about 90 seconds for 100 million rows in the source table. The query runs longer than necessary because some amount of time is wasted on the client discarding all of those rows.

It's not clear to me if you need ordered results or what you plan on doing with such a large result set. The query can be adjusted to meet the actual scenario. The biggest advantage of this approach is that it does not require a sort in the query plan. That can help for larger result sets. One disadvantage is that performance will not be optimal if there are a lot of NULLs in the table because many rows will be read from the index and discarded. You should be able to improve performance with a filtered index that excludes NULLs for that case.

Sample data for the test:

DROP TABLE IF EXISTS #t;

CREATE TABLE #t (
ID BIGINT NOT NULL
);

INSERT INTO #t WITH (TABLOCK)
SELECT TOP (10000) ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) - 1
FROM master..spt_values t1
CROSS JOIN master..spt_values t2
OPTION (MAXDOP 1);

DROP TABLE IF EXISTS dbo.[BIG_TABLE(FOR_U)];

CREATE TABLE dbo.[BIG_TABLE(FOR_U)] (
ID BIGINT NOT NULL,
[VALUE] BIGINT NULL
);

INSERT INTO dbo.[BIG_TABLE(FOR_U)] WITH (TABLOCK)
SELECT 10000 * t1.ID + t2.ID, CASE WHEN (t1.ID + t2.ID) % 3 = 1 THEN t2.ID ELSE NULL END
FROM #t t1
CROSS JOIN #t t2;

CREATE UNIQUE CLUSTERED INDEX ADD_ORDERING ON dbo.[BIG_TABLE(FOR_U)] (ID);

One method, by using OVER() and MAX() and COUNT() based on this source could be:

SELECT ID, MAX(value) OVER (PARTITION BY Value2) as value
FROM
(
 SELECT ID, value
 ,COUNT(value) OVER (ORDER BY ID) AS Value2
 FROM dbo.HugeTable
) a
ORDER BY ID;

Result

Id UpdatedValue
1 136
2 136
3 650
4 650
5 650
6 650
7 954
8 954
9 104
10 104

Another method based on this source, closely related to the first example

;WITH CTE As 
( 
SELECT value,
 Id, 
 COUNT(value) 
 OVER(ORDER BY Id) As Value2 
FROM dbo.HugeTable
),

CTE2 AS ( 
SELECT Id,
 value,
 First_Value(value) 
 OVER( PARTITION BY Value2
 ORDER BY Id) As UpdatedValue 
FROM CTE 
 ) 
SELECT Id,UpdatedValue 
FROM CTE2;

A common solution to this type of problem is given by Itzik Ben-Gan in his article The Last non NULL Puzzle:

DROP TABLE IF EXISTS dbo.Example;

CREATE TABLE dbo.Example
(
 id integer PRIMARY KEY,
 val integer NULL
);

INSERT dbo.Example
 (id, val)
VALUES
 (1, 136),
 (2, NULL),
 (3, 650),
 (4, NULL),
 (5, NULL),
 (6, NULL),
 (7, 954),
 (8, NULL),
 (9, 104),
 (10, NULL);

SELECT
 E.id,
 E.val,
 lastval =
 CAST(
 SUBSTRING(
 MAX(CAST(E.id AS binary(4)) + CAST(E.val AS binary(4))) OVER (
 ORDER BY E.id
 ROWS UNBOUNDED PRECEDING),
 5, 4)
 AS integer)
FROM dbo.Example AS E
ORDER BY
 E.id;

Demo: db<>fiddle