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Dividing an array into optimum no of equal sum sublists


Finding a single subset with a given weight is NP hard. If you've some way to identify all the subsets of a given weight and whose costs are less than $300 then you need to solve an exact cover problem, which is NP hard in general. So you can't expect to find any algorithm with less than exponential complexity in the worst case.

But what I'd try here is this:

let W = total weight of all packages
let N = total number of packages
for k = 1, 2, 3, ..., N
    find all subsets of packages with weight W/k
and cost less than $300
    if there's an exact cover: stop with solution.

You can find subsets of the right weight and cost using dynamic programming assuming the number of different weights and costs are small enough. You can find exact covers using the dancing links algorithm.


Categories : Algorithm

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