Partitioning function for continuous sequences - sql

Question

There is a table of the following structure:
CREATE TABLE history
(
pk serial NOT NULL,
"from" integer NOT NULL,
"to" integer NOT NULL,
entity_key text NOT NULL,
data text NOT NULL,
CONSTRAINT history_pkey PRIMARY KEY (pk)
);
The pk is a primary key, from and to define a position in the sequence and the sequence itself for a given entity identified by entity_key. So the entity has one sequence of 2 rows in case if the first row has the from = 1; to = 2 and the second one has from = 2; to = 3. So the point here is that the to of the previous row matches the from of the next one.
The order to determine "next"/"previous" row is defined by pk which grows monotonously (since it's a SERIAL).
The sequence does not have to start with 1 and the to - from does not necessary 1 always. So it can be from = 1; to = 10. What matters is that the "next" row in the sequence matches the to exactly.
Sample dataset:
pk | from | to | entity_key | data
----+--------+------+--------------+-------
1 | 1 | 2 | 42 | foo
2 | 2 | 3 | 42 | bar
3 | 3 | 4 | 42 | baz
4 | 10 | 11 | 42 | another foo
5 | 11 | 12 | 42 | another baz
6 | 1 | 2 | 111 | one one one
7 | 2 | 3 | 111 | one one one two
8 | 3 | 4 | 111 | one one one three
And what I cannot realize is how to partition by "sequences" here so that I could apply window functions to the group that represents a single "sequence".
Let's say I want to use the row_number() function and would like to get the following result:
pk | row_number | entity_key
----+-------------+------------
1 | 1 | 42
2 | 2 | 42
3 | 3 | 42
4 | 1 | 42
5 | 2 | 42
6 | 1 | 111
7 | 2 | 111
8 | 3 | 111
For convenience I created an SQLFiddle with initial seed: http://sqlfiddle.com/#!15/e7c1c
PS: It's not the "give me the codez" question, I made my own research and I just out of ideas how to partition.
It's obvious that I need to LEFT JOIN with the next.from = curr.to, but then it's still not clear how to reset the partition on next.from IS NULL.
PS: It will be a 100 points bounty for the most elegant query that provides the requested result
PPS: the desired solution should be an SQL query not pgsql due to some other limitations that are out of scope of this question.

Answer 1

I don’t know if it counts as “elegant,” but I think this will do what you want:
with Lagged as (
select
pk,
case when lag("to",1) over (order by pk) is distinct from "from" then 1 else 0 end as starts,
entity_key
from history
), LaggedGroups as (
select
pk,
sum(starts) over (order by pk) as groups,
entity_key
from Lagged
)
select
pk,
row_number() over (
partition by groups
order by pk
) as "row_number",
entity_key
from LaggedGroups

Answer 2

Just for fun & completeness: a recursive solution to reconstruct the (doubly) linked lists of records. [ this will not be the fastest solution ]
NOTE: I commented out the ascending pk condition(s) since they are not needed for the connection logic.
WITH RECURSIVE zzz AS (
SELECT h0.pk
, h0."to" AS next
, h0.entity_key AS ek
, 1::integer AS rnk
FROM history h0
WHERE NOT EXISTS (
SELECT * FROM history nx
WHERE nx.entity_key = h0.entity_key
AND nx."to" = h0."from"
-- AND nx.pk > h0.pk
)
UNION ALL
SELECT h1.pk
, h1."to" AS next
, h1.entity_key AS ek
, 1+zzz.rnk AS rnk
FROM zzz
JOIN history h1
ON h1.entity_key = zzz.ek
AND h1."from" = zzz.next
-- AND h1.pk > zzz.pk
)
SELECT * FROM zzz
ORDER BY ek,pk
;

Answer 3

You can use generate_series() to generate all the rows between the two values. Then you can use the difference of row numbers on that:
select pk, "from", "to",
row_number() over (partition by entity_key, min(grp) order by pk) as row_number
from (select h.*,
(row_number() over (partition by entity_key order by ind) -
ind) as grp
from (select h.*, generate_series("from", "to" - 1) as ind
from history h
) h
) h
group by pk, "from", "to", entity_key
Because you specify that the difference is between 1 and 10, this might actually not have such bad performance.
Unfortunately, your SQL Fiddle isn't working right now, so I can't test it.

Answer 4

Well,
this not exactly one SQL query but:
select a.pk as PK, a.entity_key as ENTITY_KEY, b.pk as BPK, 0 as Seq into #tmp
from history a left join history b on a."to" = b."from" and a.pk = b.pk-1
declare #seq int
select #seq = 1
update #tmp set Seq = case when (BPK is null) then #seq-1 else #seq end,
#seq = case when (BPK is null) then #seq+1 else #seq end
select pk, entity_key, ROW_NUMBER() over (PARTITION by entity_key, seq order by pk asc)
from #tmp order by pk
This is in SQL Server 2008