Given an unknown array of integers of an unknown length, whose values are also unknown, how can I organize them into three columns, so that the sum of the left most group is the largest, the middle the second largest and the third is the smallest with the groups being as close as possible in size.
The actual goal here is to organize <ul> elements by their size (# of <li> elements they contain) into three columns. I'm looking for an answer in javascript, but if someone can explain the logic simply enough that would good enough :)
So in other words given an array such as...
var set = [1, 1, 4, 6, 7, 10, 3, 6]
Would be organized as...
var left = [10, 4]
var middle = [6, 7]
var right = [3, 6, 1, 1]
There are other possibilities. The first column sums to 14, but this could be the outcome of various combinations such as [6, 4, 3, 1]. Being organized in such a way would make it difficult to get the right values for the next column, so preferably use the largest numbers earlier on, as in my example above. *
I'm sure this has been asked and answered before but I didn't know how to look this up. I did some research and found out that this is pretty much the Partitioning Problem, although I'm still at a loss on how to do it or if there is simple one feasible answer here. Anything that works for the simple example I gave should suffice.
* EDIT: On second thought, this may be an incorrect assumption.
