Question

I really need an master of algorithm here! So the thing is I got for example an array like this:

[
    [870, 23]
    [970, 78]
    [110, 50]
]

and I want to split it up, so that it looks like this:

// first array
[
    [970, 78]
]
// second array
[
    [870, 23]
    [110, 50]
]

so now, why do I want it too look like this?

Because I want to keep the sum of sub values as equal as possible. So 970 is about 870 + 110 and 78 is about 23 + 50.
So in this case it’s very easy because if you would just split them and only look at the first sub-value it will already be correct but I want to check both and keep them as equal as possible, so that it’ll also work with an array which got 100 sub-arrays! So if anyone can tell me the algorithm with which I can program this it would be really great!

Scales:

• ~1000 elements (sublists) in the array
• Elements are integers up to 10^9

I am looking for a “close enough solution” – it does not have to be the exact optimal solution.

Answer 1

Thanks for all the answers, the bruteforce attack was a good idea and NP-Hard is related to this too, but it turns out that this is a multiple knapsack problem and can be solved using this pdf document.