Merging intervals in one pass in SQL

Question

Let's say I have a table with two columns: start and end, both integers, and the table is ordered by the first, then second column. Each row represents an interval.

What I need is the table of merged intervals: all overlapping or adjacent intervals gobbled up into one.

It can be constructed with a JOIN query, but that is quadratic in the number of rows, which is 4 million rows in my case (I decided to compose this question because the query is still running).

It can also be done in a single pass, by running through each row and keeping track of the maximum end time - but how to do that, or something equivalent, in standard SQL? Is there any O(n) way to do it in SQL? I'm using SQLite right now; a SQLite-specific solution would also help me out this time.

From the answers to related questions (1, 2, 3, 4, 5, 6, 7, 8, 9) I can't tell whether it's possible.

Can you?

Answer 1

Well, here is a solution that works in MySQL (I don't know if it will work in SQlite). I think, but cannot prove, that is O(n) (discarding the time it takes to sort the events table initially, i.e. if it is already sorted as I think the question states.)

> SELECT * from events;
+-------+-----+
| start | end |
+-------+-----+
|     1 |   9 |
|     5 |   8 |
|     8 |  11 |
|    11 |  13 |
|    17 |  25 |
|    18 |  26 |
|    33 |  42 |
|    59 |  81 |
|    61 |  87 |
|    97 | 132 |
|   105 | 191 |
|   107 | 240 |
|   198 | 213 |
|   202 | 215 |
+-------+-----+
14 rows in set (0.00 sec)


SET @interval_id = 0;
SET @interval_end = 0;

SELECT
  MIN(start) AS start,
  MAX(end) AS end
  FROM
    (SELECT
       @interval_id := IF(start > @interval_end,
                          @interval_id + 1,
                          @interval_id) AS interval_id,
       @interval_end := IF(start < @interval_end,
                           GREATEST(@interval_end, end),
                           end) AS interval_end,
       events.*
     FROM events
     ORDER BY start,end) tmp
  GROUP BY interval_id;

+-------+------+
| start | end  |
+-------+------+
|     1 |   13 |
|    17 |   26 |
|    33 |   42 |
|    59 |   87 |
|    97 |  240 |
+-------+------+
5 rows in set (0.00 sec)