Count up on a positive change, and down on a negative change - mysql

Question

I have a column that changes values.
I want to count by adding at each change up and subtracting at each change down. Assuming x[] are my values, Delta is the sign of change in x's elements, and y[] is my targeted results or counts.
We count up until the next delta -1 at which we start counting down, then we resume counting up when delta changes back to +1. In summary we add normally until we have a delta of -1 at that time we start subtracting, then resume adding up at the next +1 delta.
x: 1, 3, 4, 4, 4, 5, 5, 3, 3, 4, 5, 5, 6, 5, 4, 4, 4, 3, 4, 5, 6, 7, 8
Delta: 0, 1, 1, 0, 0, 1, 0, -1, 0, 1, 1, 0, 1, -1, -1, 0, 0, -1, 1, 1, 1, 1, 1
y: 1, 2, 3, 4, 5, 6, 7, 6, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9
The length of my array is in the millions of rows, and efficiency is important. Not sure if such operation should be done in SQL or whether I would be better off retrieving the data from the database and performing such calculation outside.

Answer 1

You could use this query in SQL-Server, presuming a PK-column for the ordering:
WITH CTE AS
(
SELECT t.ID, t.Value,
LastValue = Prev.Value,
Delta = CASE WHEN Prev.Value IS NULL
OR t.Value > Prev.Value THEN 1
WHEN t.Value = Prev.Value THEN 0
WHEN t.Value < Prev.Value THEN -1 END
FROM dbo.TableName t
OUTER APPLY (SELECT TOP 1 t2.ID, t2.Value
FROM dbo.TableName t2
WHERE t2.ID < t.ID
ORDER BY t2.ID DESC) Prev
)
, Changes AS
(
SELECT CTE.ID, CTE.Value, CTE.LastValue, CTE.Delta,
Change = CASE WHEN CTE.Delta <> 0 THEN CTE.Delta
ELSE (SELECT TOP 1 CTE2.Delta
FROM CTE CTE2
WHERE CTE2.ID < CTE.ID
AND CTE2.Delta <> 0
ORDER BY CTE2.ID DESC) END
FROM CTE
)
SELECT SUM(Change) FROM Changes c
The result is 9 as expected:
complete result set
only Sum
The OUTER APPLY links the current with the previous record, the previous record is the one with the highest ID < current.ID. It works similar to a LEFT OUTER JOIN.
The main challenge was the sub-query in the last CTE. That is necessary to find the last delta that is <> 0 to determine if the current delta is positive or negative.

Answer 2

You can also use LAG and SUM with OVER (Assuming you have SQL Server 2012 or above) like this.
Sample Data
DECLARE #Table1 TABLE (ID int identity(1,1), [x] int);
INSERT INTO #Table1([x])
VALUES (1),(3),(4),(4),(4),(5),(5),(3),(3),(4),(5),(5),(6),(5),(4),(4),(4),(3),(4),(5),(6),(7),(8);
Query
;WITH T1 as
(
SELECT ID,x,ISNULL(LAG(x) OVER(ORDER BY ID ASC),x - 1) as PrevVal
FROM #Table1
), T2 as
(
SELECT ID,x,PrevVal,CASE WHEN x > PrevVal THEN 1 WHEN x < PrevVal THEN -1 ELSE 0 END as delta
FROM T1
)
SELECT ID,x,SUM(COALESCE(NULLIF(T2.delta,0),TI.delta,0))OVER(ORDER BY ID) as Ordered
FROM T2 OUTER APPLY (SELECT TOP 1 delta from T2 TI WHERE TI.ID < T2.ID AND TI.x = T2.x AND TI.delta <> 0 ORDER BY ID DESC) as TI
ORDER BY ID
Output
ID x Ordered
1 1 1
2 3 2
3 4 3
4 4 4
5 4 5
6 5 6
7 5 7
8 3 6
9 3 5
10 4 6
11 5 7
12 5 8
13 6 9
14 5 8
15 4 7
16 4 6
17 4 5
18 3 4
19 4 5
20 5 6
21 6 7
22 7 8
23 8 9

Answer 3

You use sql-server and mysql tag. If this can be done within SQL-Server you should have a look on the OVER-clause: https://msdn.microsoft.com/en-us/library/ms189461.aspx
Assuming there's an ordering criteria it is possible to state a ROW-clause and use the value of a preceeding row. Many SQL-functions allow the usage of OVER.
You could define a computed column which does the calculation on insert...
Good luck!