How do I generate integer partitions?

Question

I have a list of numbers like 1,2,3 and I want to find all the combination patterns that sum up to a particular number like 5. For example:

Sum=5
Numbers:1,2         


        

Answer 1

    public static List> Partition(int n, int max, string prefix)
    {

        if (n == 0)
        {
            _results.Add(prefix.Split(new char[] { ',' }).ToList());
        }

        for (int i = Math.Min(max, n); i >= 1; i--)
        {
            Partition(n - i, i, prefix + "," + i);
        }

        return _results;
    }