How to re-arrange rows to best fit within groups?

Question

I categorized a table with the method introduced here to categorize my items to folders with a limit size of 100.

mixing_order  id     num_items  cat order_in_cat cumulative_sum folder
1             1      4          1   1            4              1
2             2      33         1   2            37             1
3             3      74         2   1            74             2
4             4      41         1   3            41             3
5             5      24         1   4            65             3
6             6      44         2   2            44             4
7             7      16         1   5            57             4
8             8      55         1   6            55             5
9             9      11         1   7            66             5
10            10     37         1   8            37             6

Now, I want to go further and re-arrange the rows to better fit within folders. Consider that the records are of two categories (indicated by column cat). We can make a better fit just by altering the order of mixing. Then, we can produce the following table as each folder has a cumulative_sum close to the folder size limit (i.e. 100 here). As you can see, the order in each category (order_in_cat) has not been changed, only the order that the rows from different categories are mixed.

mixing_order  id     num_items  cat  order_in_cat cumulative_sum folder
1             1      4          1    1            4              1
2             2      33         1    2            37             1
3             4      41         1    3            78             1
4             3      74         2    1            74             2
5             5      24         1    4            98             2
6             7      16         1    5            16             3
7             8      55         1    6            67             3
8             9      11         1    7            78             3
9             6      44         2    2            44             4
10            10     37         1    8            81             4

In other words, the mixing_order was random in order of INSERT, but now we want to re-arrange the mixing_order to best fit within folder.

Probably, we need a loop in which re-calculating SUM to find the best match out of possible choices, but I have no idea how to conduct such loop in SQL.