Is it? The first query is always O(1). The worst case for the latter query is that it must aggregate over 999,910 rows.
Consider the case where all values of 'a' are 123, and all values 'b' are 42, except 90.
At least on MSSQL, I would expect a query plan like so:
1. Index seek WHERE a = 123, yielding ~100 rows. [1]
2. Bookmark lookup with results from (1), yielding ~100 rows.
3. Filter (2) WHERE b = 42 and project date_column, yielding ~10 rows.
4. Aggregate (3) by date_column, yielding ~10 rows or less.
[1] Important caveat. I interpret this line,
Current situation, selecting about hundred rows out of a million:
....to mean selection of 100 rows from the base table, rather than projection of 100 rows in the result, post-aggregation.
But if he really means a SELECT statement that returns 100 rows, then we have no idea how selective the WHERE clause is, and my answer changes to "The query will be much slower (impact >10%)".
Regarding O(1), the first query would be some form of O(n log n) or O(log n) depending on the table/index data structures.
I hope no optimizer would say that. It is well defined that filtering, as expressed in the where clause (if it uses indexes or not) happens before group and aggregate, and that grouping happens on the result of the filtering. If the optimizer could choose one way or the other, you'd have different results. If you want to group and aggregate first, you need to explicitly express that with a subquery.
In this case, I take n = 1,000,000
The first query is likely O(log(x)) where x is number of distinct values of a. I approximated that to be O(1) relative to n.
I could be wrong here, or we could have seen different questions, or we are just interpreting the question differently.
Indexing shouldn't follow the theoretical worst case, it should follow what's actually in your table.
No, it already said it only took 100 rows, it can't get worse from that.
Now if he actually meant the final result set was 100 rows (meaning after the group by) that's different. But that's not what he actually said, so the question is misleading.