# Identify consecutive values in SQL Server

March 17, 2021

In this two-part series, we look at different solutions to a SQL problem - how to identify consecutive or non-consecutive values in a column. Also known as the Gaps and Islands problem.

Understanding the Gaps and Islands problem is useful for analyzing data that features sequences or breaks in sequences.

This post, part two of the series, will look at methods for identifying consecutive values (Islands). In part one, we explored ways to identify non-consecutive values (Gaps).

## What is the Gaps and Islands problem?

As the name implies, there are two components.

Gaps - rows where a row value does not sequentially follow another...

``````1
289
10
111516
1722``````

...and Islands - rows where a row value follows another in an unbroken succession.

``````12
891011
15161722``````

## Identifying Islands

To identify islands, there are two approaches. Use a sequence identifier to group values that are in sequence. Or identify where a sequence starts and ends. Let's look at how to do both.

### Using DENSE_RANK

We're going to use the DENSE_RANK function to help create an identifier to group values that are part of a sequence.

Begin by applying the `DENSE_RANK` function to the rows.

``````-- Data setup
DECLARE @sequences TABLE
(
value_of_interest INTEGER
)

INSERT INTO @sequences
VALUES (1),(2),(3),(6),(7),(9),(11),(12),(20),(25)

-- Solution begins
SELECT
num_sequence.value_of_interest
,DENSE_RANK() OVER(ORDER BY value_of_interest) as dense_rank_result
FROM
@sequences as num_sequence``````
``````| value_of_interest | dense_rank_result |
|-------------------|-------------------|
| 1                 | 1                 |
| 2                 | 2                 |
| 3                 | 3                 |
| 6                 | 4                 |
| 7                 | 5                 |
| 9                 | 6                 |
| 11                | 7                 |
| 12                | 8                 |
| 20                | 9                 |
| 25                | 10                |``````

To produce the group identifier, we subtract the result of `DENSE_RANK` from the row value.

As the sequence increases, the result of this calculation remains constant but then changes when a new sequence starts. We use this constant to identify the islands.

``````/* Data setup */

SELECT
num_sequence.value_of_interest
,num_sequence.value_of_interest - DENSE_RANK() OVER(ORDER BY value_of_interest) as sequence_identifierFROM
@sequences as num_sequence``````
``````| value_of_interest | sequence_identifier |
|-------------------|---------------------|
| 1                 | 0                   |
| 2                 | 0                   |
| 3                 | 0                   |
| 6                 | 2                   |
| 7                 | 2                   |
| 9                 | 3                   |
| 11                | 4                   |
| 12                | 4                   |
| 20                | 11                  |
| 25                | 15                  |``````

To find the sequence start and end, we subquery the result set and aggregate it by the sequence identifier.

If we were doing analysis, at this point, we have enough to summarize a sequence, e.g., `COUNT`, `AVG`, etc.

``````/* Data setup */

SELECT
MIN(sequences.value_of_interest) as sequence_started    ,MAX(sequences.value_of_interest) as sequence_startedFROM
(
SELECT
num_sequence.value_of_interest
,num_sequence.value_of_interest - DENSE_RANK() OVER(ORDER BY value_of_interest) as sequence_identifier    FROM
@sequences as num_sequence
) as sequences
GROUP BY
sequence_identifier``````
``````| sequence_started | sequence_started |
|------------------|------------------|
| 1                | 3                |
| 6                | 7                |
| 9                | 9                |
| 11               | 12               |
| 20               | 20               |
| 25               | 25               |``````

If you need to exclude sequences with only 1 row, include the `HAVING` clause filtering for row counts greater than 1.

``````/* Data setup */

SELECT
MIN(sequences.value_of_interest) as sequence_start
,MAX(sequences.value_of_interest) as sequence_end
FROM
(
SELECT
num_sequence.value_of_interest
,num_sequence.value_of_interest - DENSE_RANK() OVER(ORDER BY value_of_interest) as sequence_identifier
FROM
@sequences as num_sequence
) as sequences
GROUP BY
sequence_identifier
HAVING    COUNT(*) > 1``````

If you're curious about why we're using `DENSE_RANK` and not `ROW_NUMBER`, this is to handle duplicates. The result of `DENSE_RANK` will produce the same group identifier for duplicate sequences.

### Using Subqueries, ROW_NUMBER, and CTEs

Recall from the article on Identifying Gaps that this involves working out where a sequence ends and a new one begins. We can apply the same technique to help identify islands.

This query has a few different parts, so we'll break it apart and build it into a final query.

First, let's look at the following query. It uses two similar subqueries to identify where a sequence started or ended.

``````-- Data setup
DECLARE @sequences TABLE
(
value_of_interest INTEGER
)

INSERT INTO @sequences
VALUES (1),(2),(3),(6),(7),(9),(11),(12),(20),(25)

-- Solution begins
SELECT
num_sequence_outer.value_of_interest
,(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest - 1    ) as sequence_started
,(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest + 1    ) as sequence_ended
FROM
@sequences as num_sequence_outer``````

Notice that we get `NULL` in the columns when a sequence starts or ends.

``````| value_of_interest | sequence_started | sequence_ended |
|-------------------|------------------|----------------|
| 1                 | NULL             | 2              |
| 2                 | 1                | 3              |
| 3                 | 2                | NULL           |
| 6                 | NULL             | 7              |
| 7                 | 6                | NULL           |
| 9                 | NULL             | NULL           |
| 11                | NULL             | 12             |
| 12                | 11               | NULL           |
| 20                | NULL             | NULL           |
| 25                | NULL             | NULL           |``````

Now we need a way to filter for the `NULL`s in the `sequence_started` and `sequence_ended` columns.

To do this, we move the subquery into the `WHERE` clause and combine it with `NOT EXISTS`. This condition filters for rows where the subquery returns `NULL`.

``````/* Data setup */

-- sequence starts
SELECT
num_sequence_outer.value_of_interest
FROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest - 1    )

-- sequence endings
SELECT
num_sequence_outer.value_of_interest
FROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest + 1    )``````

At this point, we're still working with two separate result sets—a set of sequence starting points and a set of sequence ending points.

``````| value_of_interest |   | value_of_interest |
|-------------------|   |-------------------|
| 1                 |   | 3                 |
| 6                 |   | 7                 |
| 9                 |   | 9                 |
| 11                |   | 12                |
| 20                |   | 20                |
| 25                |   | 25                |``````

Because each result set contains equal rows, we can connect them with the `ROW_NUMBER` function.

``````/* Data setup */

SELECT
num_sequence_outer.value_of_interest
,ROW_NUMBER() OVER(ORDER BY value_of_interest) as row_nFROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest - 1
)

SELECT
num_sequence_outer.value_of_interest
,ROW_NUMBER() OVER(ORDER BY value_of_interest) as row_nFROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest + 1
)``````
``````| value_of_interest | row_n |   | value_of_interest | row_n |
|-------------------|-------|   |-------------------|-------|
| 1                 | 1     |   | 3                 | 1     |
| 6                 | 2     |   | 7                 | 2     |
| 9                 | 3     |   | 9                 | 3     |
| 11                | 4     |   | 12                | 4     |
| 20                | 5     |   | 20                | 5     |
| 25                | 6     |   | 25                | 6     |``````

To finish, we put each result set in a Common Table Expression (CTE) and combine them based on their row numbers. A temp table would also work in this situation.

``````/* Data setup */

;
WITH sequence_starts AS    (
SELECT
num_sequence_outer.value_of_interest
,ROW_NUMBER() OVER(ORDER BY value_of_interest) as row_num
FROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest - 1
)
),
sequence_ends AS (        SELECT
num_sequence_outer.value_of_interest
,ROW_NUMBER() OVER(ORDER BY value_of_interest) as row_num
FROM
@sequences as num_sequence_outer
WHERE NOT EXISTS
(
SELECT
num_sequence_sub.value_of_interest
FROM
@sequences as num_sequence_sub
WHERE
num_sequence_sub.value_of_interest = num_sequence_outer.value_of_interest + 1
)
)

SELECT
sequence_starts.value_of_interest as island_start
,sequence_ends.value_of_interest as island_ends
FROM
sequence_starts
INNER JOIN sequence_ends
ON sequence_starts.row_num = sequence_ends.row_num``````

If you only want sequences with more than 1 row, filter for rows where the sequence's start and end are not the same value.

``````-- ...

SELECT
sequence_starts.value_of_interest as island_start
,sequence_ends.value_of_interest as island_ends
FROM
sequence_starts
INNER JOIN sequence_ends
ON sequence_starts.row_num = sequence_ends.row_num
WHERE
sequence_starts.value_of_interest <> sequence_ends.value_of_interest``````
``````| island_start | island_ends |
|--------------|-------------|
| 1            | 3           |
| 6            | 7           |
| 11           | 12          |``````

Lastly, as an interesting side note, if we modify the join, it's possible to arrive at the gaps!

``````-- ...

SELECT
sequence_ends.value_of_interest + 1 as sequence_ends
,sequence_starts.value_of_interest - 1 as sequence_start
FROM
sequence_starts
INNER JOIN sequence_ends
ON sequence_starts.row_num = sequence_ends.row_num + 1``````
``````| sequence_ends | sequence_start |
|---------------|----------------|
| 4             | 5              |
| 8             | 8              |
| 10            | 10             |
| 13            | 19             |
| 21            | 24             |``````

## Conclusion

In this post, we looked at solutions to the Islands part of the Gaps and Islands problem.

An aspect we didn't examine is the performance of each solution. I opted to avoid this to focus on ways to solve the problem.

If you're interested in the performance aspects, I highly recommend the book SQL Server MVP Deep Dives. Chapter 5, Gaps and Islands, by Itzik Ben-Gan, explores the Gaps and Islands solutions in substantial detail.

For the solutions to the Gaps problem, see the previous post in this series.