Given a set s of integers, an integer total, and a non-negative integer budget, the subsetsumsearch problem is to find a subset of s, containing at most budget elements, that sums to total or to report that no such set exists. given a set s of integers and an integer total, the subsetsumoptimization problem is to find the smallest subset of s that sums to total or to report that no such set exists. a) suppose you have a polynomial time algorithm called sss that solves the subsetsumsearch problem. describe, in clear and concise english, a polynomial time algorithm called sso that solves the subsetsumoptimization problem. (hint: sso should call sss multiple times.) b) suppose s is a set containing n integers, and that sss(s, total, budget) is o(g( what of these is the tightest upper bound on the running time of sso(s, total)? a. o(g(n^2)) b. o(g(n)^2) c. o(g(log n)) d. o(g(n) log n)