[閒聊] proof of NPC of the group-summation problem
Problem P:
Let C be a natural integer set {c1, c2 .. cn}
given a function e(x), try to partition C in to some groups G1, G2 .. Gm
such that Σe(Gi) is minimal, where e(Gi) = e(Σ(c in Gi)),
answer is the minimal value of Σe(Gi).
P can be reduced to a partition problem:
Let H =Σci/2, set e(H) = 0 and e(x) = 1 for all x != H
then P's answer is 0 iff C can be divided into two
parts and the sum of each part are equal.
Since the partition problem is NPC, so is P
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