Hourly counting based on start time and end time data

Question

In the table, the data is in timestamp format but I am sharing it in time(start_at) and time(end_at) format.

Table structure:

id, start_at, end_at
1, 03:00:00, 06:00:00
2, 02:00:00, 05:00:00
3, 01:00:00, 08:00:00
4, 08:00:00, 13:00:00
5, 09:00:00, 21:00:00
6, 13:00:00, 16:00:00
6, 15:00:00, 19:00:00

For the result, we need to count the number of active ids between the start_at and end_at times.

hours, count
0, 0
1, 1
twenty two
3, 3
4, 3
5, 2
6, 1
7, 1
8,1
9, 2
10, 2
11, 2
12, 2
13, 3
14, 2
15, 3
16, 2
17, 2
18, 2
19,1
20,1
21,0
22,0
23, 0

Answer 1

or

WITH RECURSIVE
cte AS (
    SELECT 0 `hour`
    UNION ALL
    SELECT `hour` + 1 FROM cte WHERE `hour` < 23
)
SELECT cte.`hour`, COUNT(test.id) `count`
FROM cte 
LEFT JOIN test ON cte.`hour` >= HOUR(test.start_at)
              AND cte.`hour` < HOUR(test.end_at)
GROUP BY 1
ORDER BY 1;

or

WITH RECURSIVE
cte AS (
    SELECT CAST('00:00:00' AS TIME) `hour`
    UNION ALL
    SELECT `hour` + INTERVAL 1 HOUR FROM cte WHERE `hour` < '23:00:00'
)
SELECT cte.`hour`, COUNT(test.id) `count`
FROM cte 
LEFT JOIN test ON cte.`hour` >= test.start_at 
              AND cte.`hour` < test.end_at 
GROUP BY 1
ORDER BY 1;

The first query returns the hour column in time format, while the second query returns this column in numeric form. Choose the variant that is safe for you.

https://dbfiddle.uk/?rdbms=mysql_8.0&fiddle=5a77b6e3158be06c7a551cb7e64673de