Explain this subset sum solving function [duplicate]

问题

This chunk of code is the function that solves a variant of a subset sum problem, but I dont really understand how it gets the answer.

The function returns the subset sum that's closest to the value, if its the same as the value then it just return the value, if two subsets sums are equally close to the value then return the greater sum.

This is it

public static List<int> SolveSubsetSum(int value, IEnumerable<int> xs) 
{
    int b = 2*value+1;
    List<int>[] cols = new List<int>[b];
    cols[0] = new List<int>();
    foreach(int xi in xs) {
        for(int s = b-xi-1; s >= 0; s--) {
            if(cols[s+xi] == null && cols[s] != null) {
               List<int> cln = new List<int>(cols[s]);
               cln.Add(xi);
               cols[s+xi] = cln;
            }
        }
    }
    for(int d = 0; d <= value; d++) {
        if(cols[value+d] != null) {
            return cols[value+d];
        }
        else if(cols[value-d] != null) {
            return cols[value-d];
        } 
    }
    return cols[0];
}

I understand the standard stuff, but I have no clue whats going on in the loops.

My main questions are

Why does it need an array of 2*value+1 collections ?
Whats going on in the loops ?

回答1:

Somehow, the code in your question is an exact copy of this (my¹) answer that implemented this algorithm. I agree that the algorithm itself is not new, but both the structure of the code as well as the variables indicate copying. If you had read the question (and answer) carefully, you could have found out that the problem being solved is the closest subset sum problem. This means that in case no such set can be constructed, you return the set with the smallest difference.

Now since such set can be larger that the requested sum, you need at most 2 K+1 collections with K the requested number, because it is possible that the smallest number in your collection is K-1. Say for instance that the given numbers are {2,5,8,10} and you wish to construct a subset of 6, than the nearest subset sum is {2,5}. You need enough "collections" to store subsets that can be larger.

What's going on in the loops is explain in the linked answer.

¹ Who wrote the answer is irrelevant, nevertheless is it easier to detect your own work.

来源：https://stackoverflow.com/questions/34275612/explain-this-subset-sum-solving-function

标签

algorithm

subset-sum