How to split a list of items into equal partitions according to the item's weight?

Question

I have a list of items that is somewhat like this:

[
  [\"orange\", 9],
  [\"watermelon\", 3],
  [\"grapefruit\", 6],
  [\"peach\", 8],
  [\"durian\", 2],
           


        

Answer 1

This is the optimization version of the partition problem, which is NP-complete, although, according to that article, "there are heuristics that solve the problem in many instances, either optimally or approximately."

The methods section of that article contains a number of ways to do approximate or pseudo-polynomial solutions. Specifically, if you can live with an approximate answer, you could try the greedy approach:

One approach to the problem, imitating the way children choose teams for a game, is the greedy algorithm, which goes through the numbers in descending order, assigning each of them to whichever subset has the smaller sum.

The running time of this approach is O(n^2) and is guaranteed to get you to within a factor of 4/3 of the exact solution.

If you must have an exact solution and your data set is small enough, you could always take a brute force approach of generating every possibility (this is exponential, O(2^n)). Depending on your performance needs, this might be sufficient.