Say we have a constant-time function that accepts some integer set. The function outputs True if we can split the integers into two subsets of an equal sum. If we can't partition the integers given, the function outputs False.
Suppose we can use this function at any time, with any set of integers. Can we make a greedy algorithm using this function that will output one of the specific subsets that sum to half of a particular positive integer set?
The heart of the question: If we know at any time the boolean result of canPartition() on any set of integers, can we greedily use that to output the specific values of a partition?