How can I get the maximum sequential in number range? - sql

Question

I have the specific result above in a select:
1 2
1 3
1 5
1 6
1 9
1 10
1 11
1 13
1 14
1 16
1 18
1 20
1 23
1 24
1 25
What I want to find is the longest increasing-by-one chain that occurs in the results.
For example, I know that 3 is the maximum length sequence in this number range, coming from the last 3 results (23,24,25 being 3 in a row).

Answer 1

A sequence will have the property that the difference between the number and a sequential ordering will be constant. In most dialects of SQL, you have a function called row_number(), which assigns sequential numbers.
We can use this observation to solve your problem:
select (num - seqnum), count(*) as NumInSequence
from (select t.*, row_number() over (order by num) as seqnum
from t
) t
group by (num - seqnum)
This gives every sequence. To get the max, either use max() with a subquery or some version of limit/top. In SQL Server, for instance, you can do:
select top 1 count(*) as NumInSequence
from (select t.*, row_number() over (order by num) as seqnum
from t
) t
group by (num - seqnum)
order by NumInSQuence desc

Answer 2

Using this article as the main query:
http://www.xaprb.com/blog/2006/03/22/find-contiguous-ranges-with-sql/
Just add a column that calculates the difference and select the MAX().
SELECT MAX(seq.end - seq.start)
FROM (
select l.id as start,
(
select min(a.id) as id
from sequence as a
left outer join sequence as b on a.id = b.id - 1
where b.id is null
and a.id >= l.id
) as end,
from sequence as l
left outer join sequence as r on r.id = l.id - 1
where r.id is null;
) AS seq

Answer 3

#Gordon gave a brilliant and more terse answer. However, I think a recursive implementation may be useful as well. Here's a very useful article on recursive CTEs: http://msdn.microsoft.com/en-us/library/ms186243(v=sql.105).aspx
-- This first CTE is unnecessary because you presumably already have
-- your data. But I wanted to include it to make it easier test.
WITH myNumbers AS (
SELECT *
FROM (
VALUES
(2),
(3),
(5),
(6),
(9),
(10),
(11),
(13),
(14),
(16),
(18),
(20),
(23),
(24),
(25)
) AS x (num)
),
-- To get my sequences I recurse until there is no num + 1 in my set
mySequences AS (
-- Anchor member definition: Create the first invocation
SELECT v.num, 0 AS iteration, v.num AS previous, v.num AS start
FROM myNumbers v
UNION ALL
-- Recursive member definition: Recurse until value + 1 does not exist
SELECT s.num + 1, s.iteration + 1 AS iteration, s.num AS previous, s.start
FROM mySequences s -- Notice that we can reference the CTE within itself
JOIN myNumbers v
ON v.num = s.num + 1
)
-- I must increment by 1 because I chose to start my recursion at 0
SELECT MAX(iteration + 1)
FROM mySequences
That recursive query is similar to writing
public int GetSequenceLength(int start, int iteration, int[] myNumbers)
{
if (myNumbers.Contains(start + 1))
{
return GetSequenceLength(start + 1, iteration + 1, myNumbers);
}
return iteration;
}
foreach (var myNumber in myNumbers)
{
var sequenceLength = GetSequenceLength(myNumber, 0, myNumbers) + 1;
Console.WriteLine(myNumber + " : " + sequenceLength);
}