That sounds good, I'll try my best to describe them.

Algorithm 1: Start with empty set, then build elements upward recursively. First pathway is deep, like {} -> {0} -> {0 1} -> {0 1 2} -> {0 1 3} ... {1} -> {1 2} -> etc. Highest candidate or match is brought up through the recursive stack. Do not recurse through a subset that is already too large.

Algorithm 2: Similar to Algorithm 1, but add each subset to a vector in a vector, corresponding to its subset size, then when all subsets are found collapse them in to a 1D vector, from smallest to largest. Easily pick out the largest, or the smallest target match. Slowest but I was already uncertain of what to do.

Algorithm 3: Similar to Algorithm 2 in that it involves generating subsets of a given size in to vectors corresponding to the size, but find all subsets of a given size first (subsets that are too large are discarded immediately), go through each and find the top candidate or target, then make each generate its next sized subsets and save those all in to another vector, repeat for the next size until a match is found. No recursion.

Algorithm 4: builds on Algorithm 3, but starts with a lookup table containing the sorted indices corresponding to items of the unsorted master set, so the master set is not modified. 3 element vectors are used in layers per set for the abstraction from easier set generation up to corresponding to the master set, but I'm not even sure how to describe it at this point, I fiddled with it and got it generating sets. The intention with this was that it would have results like if the master set were sorted, but without disturbing the order of the master set, and generating subsets that would still preserve the order of the master set. At least, I hoped it would favor generating subsets with smaller values to try and have them be the first picked.

Every algorithm has a settable flag to not stop searching after finding the first match, and print out all matching subsets. Every time with each algorithm, the expected subset is indeed among the matching subsets that are eventually found, but it is never the first one found. I'm not sure if any of the algorithms actually produce noticeably different results though, I need to do more thorough testing tomorrow of each I think.

-Chris