I'm a little lost and don't know how to approach this problem.
Show the partition search problem can be poly-time reduced to the partition decision problem, the partition decision problem takes an input set of numbers and returns true if there is a subset of the initial set that sums up to half the total sum of the initial set.
With problems like ham-path search, clique search and SAT search, the key was to build the solution one piece at a time using the results from the decision "oracle". But I need to know how to approach this problem.
Initially, I thought about removing elements from the set while verifying if there is a partition in the remaining set, which led me nowhere. Now I'm wondering if adding elements to the initial set would have any results. I noticed if the initial set has a partition, adding elements to the set would then only have a partition if the added element is even, but I don't see how this can generate a subset of the original set that satisfies partition search. Am I going off the wrong track? Any pointers would be appreciated.