A university network is composed of N computers. System administrators gathered information on the traffic between nodes, and carefully divided the network into two subnetworks in order to minimize traffic between parts.
A disgruntled computer science student Vasya, after being expelled
from the university, decided to have his revenge. He hacked into the
university network and decided to reassign computers to maximize the
traffic between two subnetworks.
Unfortunately, he found that calculating such worst subdivision is
one of those problems he, being a student, failed to solve. So he asks
you, a more successful CS student, to help him.
The traffic data are given in the form of matrix C, where Cij is the
amount of data sent between ith and jth nodes (Cij = Cji, Cii = 0). The
goal is to divide the network nodes into the two disjointed subsets A
and B so as to maximize the sum ∑Cij (i∈A,j∈B).