3-PARTITION problem

Question

here is another dynamic programming question (Vazirani ch6)

Consider the following 3-PARTITION problem. Given integers a1...an, we want to determine whet

Answer 1

I think by reduction it goes like this:

Reducing 2-partition to 3-partition:

Let S be the original set, and A be its total sum, then let S'=union({A/2},S). Hence, perform a 3-partition on the set S' yields three sets X, Y, Z. Among X, Y, Z, one of them must be {A/2}, say it's set Z, then X and Y is a 2-partition. The witnesses of 3-partition on S' is the witnesses of 2-partition on S, thus 2-partition reduces to 3-partition.