mincut.cpp

// Adjacency matrix implementation of Stoer-Wagner min cut algorithm. Runs in O(V^3).
// Note, this is NOT min s-t cut, which is solved by max flow. This finds a global cut in an *undirected* graph.

typedef vector<int> VI;
typedef vector<VI> VVI;

const int INF = 1000000000;

// return value: (min cut value, nodes in half of min cut)
pair<int, VI> GetMinCut(VVI &weights) {
  int N = weights.size();
  VI used(N), cut, best_cut;
  int best_weight = -1;
  
  for (int phase = N-1; phase >= 0; phase--) {
    VI w = weights[0];
    VI added = used;
    int prev, last = 0;
    for (int i = 0; i < phase; i++) {
      prev = last;
      last = -1;
      for (int j = 1; j < N; j++)
        if (!added[j] && (last == -1 || w[j] > w[last])) last = j;
      if (i == phase-1) {
        for (int j = 0; j < N; j++)
                weights[prev][j] += weights[last][j];
        for (int j = 0; j < N; j++)
                weights[j][prev] = weights[prev][j];
        used[last] = true;
        cut.push_back(last);
        if (best_weight == -1 || w[last] < best_weight) {
          best_cut = cut;
          best_weight = w[last];
        }
      } else {
        for (int j = 0; j < N; j++)
          w[j] += weights[last][j];
        added[last] = true;
      }
    }
  }
  return make_pair(best_weight, best_cut);
}