March 20, 2006 at 1:58 pm
Comments posted to this topic are about the content posted at http://www.sqlservercentral.com/columnists/slasham/findinggapsinasequentialnumbersequence.asp
April 3, 2006 at 8:32 am
If you just need to identify IF a list of numbers is in sequence, but not where the gaps are, I believe you can do it in a single pass of the table. (Warning -- to understand this algorithm, some high school math is required!)
-- Mathematical way of identifying if a list of numbers is sequential
-- Based on formula:
-- M + (M+1) + (M+2) + ... + (M+n-1) = n*M + n*(n-1)/2
-- Calling the left side S (for Sum), and rearranging yields:
-- n2 + (2*M - 1)*n - 2*S = 0
-- Then the quadratic formula produces:
-- n = ( (1-2*M) +- sqrt( (2*M -1)2 + 8*S) )/2
-- I believe it can be shown that a list of numbers is a sequence if
-- and only if the value in the sqrt() above is a perfect square.
-- The code below is based on that assumption
--
-- Mike Arney, 4/3/2006
set
nocount on
create
table Numbers (id int not null)
insert
Numbers values (6)
insert
Numbers values (7)
insert
Numbers values (8)
insert
Numbers values (9)
insert
Numbers values (10)
insert
Numbers values (11)
insert
Numbers values (12)
-- insert Numbers values (14) -- uncomment for testing
declare
@Sum bigint, @Count bigint, @min-2 bigint
select
@Sum = sum(convert(bigint, id)), @Count = count(*), @min-2 = min(id) from Numbers
declare
@sqrt float
select
@sqrt = sqrt( power((2*@min-2 - 1), 2) + 8*@Sum)
if
@sqrt = floor(@sqrt) select 'Sequence' else select 'Not Sequence'
go
drop
table Numbers
go
April 3, 2006 at 9:07 am
A self join solution:
select a.SeqNumber, max(b.SeqNumber)
from #SequenceTable a join #SequenceTable b on a.SeqNumber > b.SeqNumber
group by a.SeqNumber
having a.SeqNumber - max(b.SeqNumber) > 1
April 3, 2006 at 11:19 am
This way is a few hundred times faster (on large datasets)...NOTE:the details are missing but it still identifies the key holes in the sequence, except beiging and end which are obvious...?
SELECT s1.SeqNumber
FROM #SequenceTable s1
LEFT JOIN #SequenceTable s2
ON s1.SeqNumber = s2.SeqNumber -1
WHERE s2.SeqNumber IS NULL
April 3, 2006 at 2:34 pm
I agree, the join on "where Seq2.SeqNumber < Seq1.SeqNumber" will be a killer with large tables.
This version uses a simple a = b-1 join to find the gaps, then a subquery to find the last value before the gap. On 1 million rows it ran in 1/4 the elapsed time and 1/13 the CPU time of the original in the article.
select
LastSeqNumber, NextSeqNumber
, FirstAvailable = LastSeqNumber + 1
, LastAvailable = NextSeqNumber - 1
, NumbersAvailable = NextSeqNumber - (LastSeqNumber + 1)
from (
select (SELECT TOP 1 SeqNumber FROM #SequenceTable WHERE SeqNumber < a.SeqNumber ORDER BY SeqNumber DESC) as LastSeqNumber,
a.SeqNumber as NextSeqNumber
from #SequenceTable a
left join #SequenceTable b on a.SeqNumber = b.SeqNumber + 1
where b.SeqNumber IS NULL
) a
order by LastSeqNumber
April 5, 2006 at 8:52 am
Nice solution!
I would like to contribute too. If we only want to find IF there is a gap in the sequence we only need to verify that COUNT(*) + MIN(ID) = MAX(ID), right?
In that case, if we have an index on the ID columns we only need a quick scan on it with very little additional CPU+Memory usage with:
create table Numbers (id int not null)
insert Numbers values (6)
insert Numbers values (7)
insert Numbers values (8)
-- insert Numbers values (14) -- uncomment for testing
-- DELETE Numbers WHERE id = 14
SELECT CASE WHEN COUNT(*) + MIN(ID) - 1 = MAX(ID) THEN 'Sequence' ELSE 'Not Sequence' END FROM NUMBERS
go
drop table Numbers
April 27, 2006 at 3:51 pm
Thanks all for the great examples of other ways to get the same results. It is interesting to see these different methods and the understandings of how SQL works under the hood so to speak, with different timings on the various methods. For me timing was not a big issue, and my 31 second run over a table of 3.5 million rows seemed fair. Timing becomes more significant if a process is being repetatively and frequently run.
Over my dataset, Scott Coleman’s method ran in 25 seconds, being significantly slower than his own reported difference, indicating other factors come into play.
Brendan Smith’s method ran in 10 seconds, and although I accept this is faster, it does not do the computes for the additional rows in my output set, so is not a reliable comparison, but looks promising.
Mike Gress’s example did not complete, I bombed it off at over 14 minutes with no results (sorry Mike).
I didn’t try Hanslindgren’s method as it is not my database, so I was unable to add indexes to it.
To Mike Arney, my high school maths was never that good, but I am sure there will be some that can work this one out from your example.
Joe Celko’s second method also did not complete, and I bombed this off at over 14 minutes with no results, and Joe’s first method took less than a second and produced no results (sorry Joe).
Looking deeper at my source dataset, the timing differences I get to your own results may be due to the extreme number of gaps. My data set produced 1.1 million rows (of identified gaps). Also within my data set are sequence number duplications, which may have contributed to the failure of some of the scripts.
Thanks you all for your feedback and suggestions.
Stephen
April 28, 2006 at 4:02 am
Hi Stephen!
Thank you, it is not always you get such an exhausting feedback of how things turn out when you post replies and hope you can help.
Hanslindgren
April 3, 2007 at 2:59 am
Hi,
I'm a latecomer to the party and didn't realize there had already been healthy debate, but here's what I came up with.
Looking through the previous submissions above, it's the same concept as Brendan's, but extended to support the full functionality of the original post.
For the original example (working on an unoptimized temp table) the time taken seems to be approx 0.25 secs/1000 records, so with 10000 records I'm getting something like 3 seconds run time. With the code below there seems to be no increase in time taken at all (around 0.25 secs for anything from 0 to 10000 records), but this is probably because for small datasets the main delay below is not due to the work itself, but rather the creation of the temp table.
I'd be interested to see if anyone can make something faster! (ignoring the fact that I could probably have made it a table variable...)
Thanks,
Tao
CREATE TABLE #StartsAndEnds (EventID Int, EventType NVarChar(20), IdentityTracker INT IDENTITY (1,1))
INSERT INTO #StartsAndEnds (EventID, EventType)
SELECT SeqNumber, Type
FROM (
SELECT Seq1.SeqNumber, 'Start' AS Type
FROM #SequenceTable Seq1
LEFT JOIN #SequenceTable Seq2 ON Seq2.SeqNumber = Seq1.SeqNumber + 1
WHERE Seq2.SeqNumber Is Null
UNION ALL
SELECT Seq1.SeqNumber, 'End' AS Type
FROM #SequenceTable Seq1
LEFT JOIN #SequenceTable Seq2 ON Seq2.SeqNumber = Seq1.SeqNumber - 1
WHERE Seq2.SeqNumber Is Null
) AS PingPong
ORDER BY SeqNumber
SELECT IsNull(FL1.EventID, 0) AS StartGap,
FL2.EventID As EndGap,
IsNull(FL1.EventID, 0) + 1 AS FirstAvailable,
FL2.EventID - 1 AS LastAvailable,
FL2.EventID - IsNull(FL1.EventID, 0) - 1 As AvailableCount
FROM #StartsAndEnds FL2
LEFT JOIN #StartsAndEnds FL1 ON FL2.IdentityTracker = FL1.IdentityTracker + 1
WHERE FL2.IdentityTracker % 2 = 1
DROP TABLE #StartsAndEnds
http://poorsql.com for T-SQL formatting: free as in speech, free as in beer, free to run in SSMS or on your version control server - free however you want it.
April 3, 2007 at 2:11 pm
Hi Tao, did you post the correct version of your code?
I copied your code above and did a find/replace on #SequenceTable and SeqNumber swapping these for my table name and sequence field respectively, then ran it. It was certainly quick, very impressive, 16 seconds to produce 142874 identified breaks in the sequence from a table containing 3,827,625 rows.
First few rows of output are as below
| StartGap | EndGap | FirstAvailable | LastAvailable | AvailableCount | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 0 | NULL | 1 | NULL | NULL | ||||
| 58224 | 62107 | 58225 | 62106 | 3882 | ||||
| 78025 | 80086 | 78026 | 80085 | 2060 |
My original query over the same table takes 44 seconds and produces the following first few rows.
| StartGap | EndGap | FirstAvailable | LastAvailable | AvailableCount | ||||
| 0 | 2 | 1 | 1 | 1 | ||||
| 20624 | 20626 | 20625 | 20625 | 1 | ||||
| 52091 | 52093 | 52092 | 52092 | 1 | ||||
| 55518 | 55520 | 55519 | 55519 | 1 | ||||
| 58222 | 58224 | 58223 | 58223 | 1 | ||||
| 62107 | 78025 | 62108 | 78024 | 15917 | ||||
| 80086 | 80088 | 80087 | 80087 | 1 | ||||
| 80160 | 80162 | 80161 | 80161 | 1 | ||||
I've checked the results and my query is showing the correct gaps. Your result line showing 58224 to 62107 represents my end gap result line 5 above to my start gap result line 6 above.
Love to see your revision as certainly looks like it will be very fast.
Stephen
January 5, 2010 at 8:46 pm
Thanks for your all excellent solutions. Much appreciated!
July 2, 2011 at 11:35 am
Mike Arney (4/3/2006)
If you just need to identify IF a list of numbers is in sequence, but not where the gaps are, I believe you can do it in a single pass of the table. (Warning -- to understand this algorithm, some high school math is required!)<FONT color=#008000 size=2>
Or some grade school one:
SELECT CASE WHEN COUNT(Id) = MAX(Id) - MIN(Id) + 1 THEN 'In sequence' ELSE 'Not sequence' END FROM yourtable
😀
July 2, 2011 at 11:50 am
Here is another thing i found and modified a little.
Takes under a second for 1 millon rows and returns gaps size sorted 😉
Change tables and fields surrounded by []
----------------------------------------
SELECT
LastSysId + 1 AS GapFrom,
NextSysId - 1 AS GapTo,
NextSysId - (LastSysId + 1) AS GapSize
FROM
(
SELECT
(
SELECT TOP 1
[SysId]
FROM
[yourtable]
WHERE
[SysId] < a.[SysId]
ORDER BY
[SysId] DESC
) AS LastSysId,
a.[SysId] AS NextSysId
FROM
[yourtable] AS a
LEFT JOIN
[yourtable] AS b ON a.[SysId] = b.[SysId] + 1
WHERE
b.[SysId] IS NULL
) AS a
WHERE
LastSysId IS NOT NULL
ORDER BY
3 DESC
July 2, 2011 at 10:35 pm
Martin Grape (7/2/2011)
Here is another thing i found and modified a little.Takes under a second for 1 millon rows and returns gaps size sorted 😉
Change tables and fields surrounded by []
----------------------------------------
SELECT
LastSysId + 1 AS GapFrom,
NextSysId - 1 AS GapTo,
NextSysId - (LastSysId + 1) AS GapSize
FROM
(
SELECT
(
SELECT TOP 1
[SysId]
FROM
[yourtable]
WHERE
[SysId] < a.[SysId]
ORDER BY
[SysId] DESC
) AS LastSysId,
a.[SysId] AS NextSysId
FROM
[yourtable] AS a
LEFT JOIN
[kicks_medlem_20110630] AS b ON a.[SysId] = b.[SysId] + 1
WHERE
b.[SysId] IS NULL
) AS a
WHERE
LastSysId IS NOT NULL
ORDER BY
3 DESC
Nicely done and I can verify the speed. The only problem is that the code doesn't recognize missing "SysID" of 1. In fact, it doesn't recognize any gap from 1 to x-1 if all the rows between 1 to x-1 are missing. That could be OK for some folks. For me, it's usually not. It's neither wrong nor right. "It Depends" on what it's being used for.
--Jeff Moden
Change is inevitable... Change for the better is not.
July 3, 2011 at 8:24 am
Here is a little stored procedure i made out of this that will return a list of gaps including missing 1-x (or 0-x or whatever-x) or
return the first available number i a sequence. Njoy :hehe:
-- Drop procedure if it exists
IF EXISTS (SELECT * FROM [sys].[objects] WHERE OBJECT_ID = OBJECT_ID(N'[dbo].[FindGap]') AND [type] IN (N'P', N'PC')) DROP PROCEDURE [dbo].[FindGap]
GO
-- Create procedure
CREATE PROCEDURE [dbo].[FindGap]
@strFindGapTable VARCHAR(254),
@strFindGapField VARCHAR(254),
@binFindGapLower BIGINT = 1,
@intFindGapMode INT = 0
AS
-- +---------------------------------------------------------------------------+
-- | |
-- | Type : SQL Procedure |
-- | Name : FindGap |
-- | Version : 1.1 |
-- | Creator : Martin Grape, ActionBase, +46 73 391 88 89 |
-- | Info : Returns first available numer in a field of sequence or |
-- | : displays a list of available gaps and number of gaps. |
-- | Input : @strFindGapTable -> Name of table to run on |
-- | : @strFindGapField -> Name of field |
-- | : @strFindGapLower -> Lower value to find gap from |
-- | : @strFindGapMode -> 0=All gaps, 1=Next available number |
-- | Example : EXEC FindGap 'yourtable', 'sysid', 1, 1 |
-- | History : 2011-07-03 Created v1.0 |
-- | : 2011-07-03 Added check for all numbers in sequence v1.1 |
-- | : |
-- | |
-- +---------------------------------------------------------------------------+
-- Declare variables
DECLARE @strFindGapSQL AS NVARCHAR(2000);
DECLARE @strFindGapPar AS NVARCHAR(2000);
DECLARE @binFindGapMin AS BIGINT;
DECLARE @binFindGapMax AS BIGINT;
DECLARE @binFindGapCount AS BIGINT;
DECLARE @binFindGapFirst AS BIGINT;
-- Make SQL to find min and max values
SET @strFindGapSQL = N'SELECT @binMinVal = MIN(' + @strFindGapField + '), @binMaxVal = MAX(' + @strFindGapField + '), @binCount = COUNT(*) FROM ' + @strFindGapTable;
SET @strFindGapPar = N'@binMinVal BIGINT OUTPUT, @binMaxVal BIGINT OUTPUT, @binCount BIGINT OUTPUT';
-- Get values into variables
EXEC SP_EXECUTESQL @strFindGapSQL, @strFindGapPar, @binFindGapMin OUTPUT, @binFindGapMax OUTPUT, @binFindGapCount OUTPUT;
-- Check mode
IF @intFindGapMode = 1
-- Next available sequence number
BEGIN
-- Check if min is bigger than supplied lower, then take that value
IF @binFindGapMin > @binFindGapLower
BEGIN
RETURN @binFindGapLower;
END
-- Check if max is smaller than supplied lower, then take that value
ELSE IF @binFindGapMax < @binFindGapLower
BEGIN
RETURN @binFindGapLower;
END
-- Check if max is the same as supplied lower, then return + 1
ELSE IF @binFindGapMax = @binFindGapLower
BEGIN
RETURN @binFindGapLower + 1;
END
-- Check if no existing gaps, return higest + 1
ELSE IF @binFindGapCount = @binFindGapMax - @binFindGapMin + 1
BEGIN
RETURN @binFindGapMax + 1
END
-- Get first available number
ELSE
BEGIN
-- Create SQL to get next value
SET @strFindGapSQL = N'SELECT TOP 1 @binMinVal = LastSysId + 1 FROM (SELECT (SELECT TOP 1 ' + @strFindGapField + ' FROM ' + @strFindGapTable + ' WHERE ' + @strFindGapField + ' < a.' + @strFindGapField + ' ORDER BY ' + @strFindGapField + ' DESC) AS LastSysId, a.' + @strFindGapField + ' AS NextSysId FROM ' + @strFindGapTable + ' AS a LEFT JOIN ' + @strFindGapTable + ' AS b ON a.' + @strFindGapField + ' = b.' + @strFindGapField + ' + 1 WHERE b.' + @strFindGapField + ' IS NULL) AS a WHERE LastSysId IS NOT NULL ORDER BY 1';
SET @strFindGapPar = N'@binMinVal BIGINT OUTPUT';
-- Get value into variable
EXEC SP_EXECUTESQL @strFindGapSQL, @strFindGapPar, @binFindGapFirst OUTPUT;
-- Return value
RETURN @binFindGapFirst;
END
END
ELSE
-- All available sequence numbers as a list
BEGIN
-- Check if first value is bigger than supplied lower, then add a row
IF @binFindGapLower < @binFindGapMin
BEGIN
-- Add a union from supplied lower to the first actual value
SET @strFindGapSQL = N'SELECT ' + CAST(@binFindGapLower AS NVARCHAR) + ' AS GapFrom, ' + CAST(@binFindGapMin - 1 AS NVARCHAR) + ' AS GapTo, ' + CAST(@binFindGapMin - @binFindGapLower AS NVARCHAR) + ' AS GapSize UNION ';
END
ELSE
BEGIN
-- Reset variable
SET @strFindGapSQL = '';
END
-- Check if to add
SET @strFindGapSQL = @strFindGapSQL + 'SELECT LastSysId + 1 AS GapFrom, NextSysId - 1 AS GapTo, NextSysId - (LastSysId + 1) AS GapSize FROM (SELECT (SELECT TOP 1 ' + @strFindGapField + ' FROM ' + @strFindGapTable + ' WHERE ' + @strFindGapField + ' < a.' + @strFindGapField + ' ORDER BY ' + @strFindGapField + ' DESC) AS LastSysId, a.' + @strFindGapField + ' AS NextSysId FROM ' + @strFindGapTable + ' AS a LEFT JOIN ' + @strFindGapTable + ' AS b ON a.' + @strFindGapField + ' = b.SysId + 1 WHERE b.' + @strFindGapField + ' IS NULL) AS a WHERE LastSysId IS NOT NULL ORDER BY 1';
-- Run the select
EXEC (@strFindGapSQL);
-- Return also the rowcount
RETURN @@ROWCOUNT;
END
-- +------------------+
-- | END OF PROCEDURE |
-- +------------------+
GO
-- +---------+
-- | Testing |
-- +---------+
-- Drop test table if it existst
IF EXISTS (SELECT * FROM [sys].[objects] WHERE OBJECT_ID = OBJECT_ID(N'[dbo].[yourtable]') AND [type] IN (N'U')) DROP TABLE [dbo].[yourtable]
GO
-- Add dummy data
SELECT 2 AS SysId INTO yourtable UNION
SELECT 6 AS SysId UNION
SELECT 8 AS SysId UNION
SELECT 9 AS SysId UNION
SELECT 11 AS SysId;
-- Example 1: Adds a row with next available number starting on 0 , displays the result table and selects next available number
DECLARE @binFindGapReturn BIGINT;
EXEC @binFindGapReturn = FindGap 'yourtable', 'sysid', 0, 1;
INSERT INTO yourtable (SysId) SELECT @binFindGapReturn
SELECT * FROM yourtable ORDER BY 1
EXEC @binFindGapReturn = FindGap 'yourtable', 'sysid', 0, 1;
SELECT @binFindGapReturn AS NextValue;
GO
-- Example 2: Returns all the gaps starting on 1 as a resultset and returns number of gaps
DECLARE @binFindGapReturn BIGINT;
EXEC @binFindGapReturn = FindGap 'yourtable', 'sysid', 1, 2;
SELECT @binFindGapReturn AS NoOfGaps;
GO
-- Example 3: Fill missing sequences to get max + 1
INSERT INTO yourtable SELECT 1
INSERT INTO yourtable SELECT 3
INSERT INTO yourtable SELECT 4
INSERT INTO yourtable SELECT 5
INSERT INTO yourtable SELECT 7
INSERT INTO yourtable SELECT 10
DECLARE @binFindGapReturn BIGINT;
EXEC @binFindGapReturn = FindGap 'yourtable', 'sysid', 0, 1;
SELECT @binFindGapReturn AS NextValue;
GO
-- Drop test table if it existst
IF EXISTS (SELECT * FROM [sys].[objects] WHERE OBJECT_ID = OBJECT_ID(N'[dbo].[yourtable]') AND [type] IN (N'U')) DROP TABLE [dbo].[yourtable]
GO
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