/**
* Computes a minimum cut of the edge-weighted graph. Precisely, it computes
* the lightest of the cuts-of-the-phase which yields the desired minimum
* cut.
*
* @param G the edge-weighted graph
* @param a the starting vertex
*/
private void minCut(EdgeWeightedGraph G, int a) {
UF uf = new UF(G.V());
boolean[] marked = new boolean[G.V()];
cut = new boolean[G.V()];
CutPhase cp = new CutPhase(0.0, a, a);
for (int v = G.V(); v > 1; v--) {
cp = minCutPhase(G, marked, cp);
if (cp.weight < weight) {
weight = cp.weight;
makeCut(cp.t, uf);
}
G = contractEdge(G, cp.s, cp.t);
marked[cp.t] = true;
uf.union(cp.s, cp.t);
}
}
/**
* Returns the cut-of-the-phase. The cut-of-the-phase is a minimum s-t-cut
* in the current graph, where {@code s} and {@code t} are the two vertices
* added last in the phase. This algorithm is known in the literature as
* <em>maximum adjacency search</em> or <em>maximum cardinality search</em>.
*
* @param G the edge-weighted graph
* @param marked the array of contracted vertices, where {@code marked[v]}
* is {@code true} if the vertex {@code v} was already
* contracted; or {@code false} otherwise
* @param cp the previous cut-of-the-phase
* @return the cut-of-the-phase
*/
private CutPhase minCutPhase(EdgeWeightedGraph G, boolean[] marked, CutPhase cp) {
IndexMaxPQ<Double> pq = new IndexMaxPQ<Double>(G.V());
for (int v = 0; v < G.V(); v++) {
if (v != cp.s && !marked[v]) pq.insert(v, 0.0);
}
pq.insert(cp.s, Double.POSITIVE_INFINITY);
while (!pq.isEmpty()) {
int v = pq.delMax();
cp.s = cp.t;
cp.t = v;
for (Edge e : G.adj(v)) {
int w = e.other(v);
if (pq.contains(w)) pq.increaseKey(w, pq.keyOf(w) + e.weight());
}
}
cp.weight = 0.0;
for (Edge e : G.adj(cp.t)) {
cp.weight += e.weight();
}
return cp;
}
