I am trying to come up with an algorithm for getting items for a news feed from several sources.

There are multiple lists of data: S1, S2, … Sn. Each of these lists has a certain known amount of items, Q1, Q2, … Qn. I need to show these items with pagination, with a certain amount from each list per page, P1, P2, … Pn, with total amount of items per page T = sum(P). I get items from lists using offset and limit (in reality, they are SQL tables). Obviously, at some point i shall run out of items of a particular type, in which case i need to fill the blanks with items from other lists to get exactly T items for each page except the last one which can have less than T items.

Here’s a concrete example for N=2, Q1=27, Q2=95, P1=10, P2=20, T=10+20=30:

==========================================================================
| Page | From S1 | S1 offset | S1 limit | From S2 | S2 offset | S2 limit |
==========================================================================
|  1   |   10    |     0     |    10    |    20   |     0     |    20    |
|  2   |   10    |    10     |    10    |    20   |    20     |    20    |
|  3   |    7    |    20     |    (7)   |    23   |    40     |    23    |
|  4   |    0    |     0     |    (0)   |    30   |    63     |    30    |
|  5   |    0    |     0     |    (0)   |     2   |    93     |    (2)   |
==========================================================================

The numbers in parenthesis are not really important, because i can live with asking the SQL table for more entries than it has.

Ideally, i’m looking for an algorithm that can give me offsets and limits for a given page.

Any ideas?