combinations or ...

[Toni]

Hello

This might be a math combination problem or alike (I can not come with a better expression in english).

I would want a set of random numbers to be matched to a sum. For example I have numbers: 9,17 and 4. Then there is another set with sum = 29. The first set has a sum of 30 while the second is 29. What I want to do is fill the second set with numbers from first until there is no more room. So in this example I would use only number 9 and 17 and leave 4 out. The remainder from set two is 3 (29 - 9 - 17 = 3). I would want this remainder to be the smallest possible.

To achieve this I thought of ordering numbers in descending order, higher numbers at the top and so on, leaving the smallest at the bottom. This way I believe I can fill the pool of the second set better with the smallest remainder possible. Do you think this is correct, is there any other better method to achieve it?

[jbante]

What you're describing is the knapsack problem. The Wikipedia pages includes descriptions of several approaches to solving it for you to consider.

[Toni]

Thank you jbante, a lot to read for today. I wish I was at my 20s again

[Fitch]

If your goal is to use the fewest items to fill the knapsack, I think your initial idea to sort the numbers descending would work. Keep in mind that you wouldn't necessarily stop when you reach a number that doesn't fit, you'd skip that one and move on to the next number, which might be small enough to fit. This would be fairly simple to do in a script using a loop.

(nice link, jb)

[Toni]

Yes Fitch, that what I was thinking. A script with loop which would tick each record that fulfills the condition. But interesting reading about knapsack nonetheless, integrating that into FM is another story.