/// <summary>
/// Find an augmenting path an alternate it's matching. If an augmenting path
/// was found then the search must be restarted. If a blossom was detected
/// the blossom is contracted and the search continues.
/// </summary>
/// <returns>an augmenting path was found</returns>
private bool Augment()
{
// reset data structures
Arrays.Fill(even, nil);
Arrays.Fill(odd, nil);
uf.Clear();
bridges.Clear();
queue.Clear();
// queue every unmatched vertex and place in the
// even level (level = 0)
for (int v = 0; v < graph.Order; v++)
{
if (subset.Contains(v) && matching.Unmatched(v))
{
even[v] = v;
queue.Enqueue(v);
}
}
// for each 'free' vertex, start a bfs search
while (!queue.IsEmpty())
{
int v = queue.Poll();
int d = graph.Degree(v);
for (int j = 0; j < d; ++j)
{
Edge e = graph.EdgeAt(v, j);
if (e.Bond == Bond.Single)
{
continue;
}
int w = e.Other(v);
if (!subset.Contains(w))
{
continue;
}
// the endpoints of the edge are both at even levels in the
// forest - this means it is either an augmenting path or
// a blossom
if (even[uf.Find(w)] != nil)
{
if (Check(v, w))
{
return(true);
}
}
// add the edge to the forest if is not already and extend
// the tree with this matched edge
else if (odd[w] == nil)
{
odd[w] = v;
int u = matching.Other(w);
// add the matched edge (potential though a blossom) if it
// isn't in the forest already
if (even[uf.Find(u)] == nil)
{
even[u] = w;
queue.Enqueue(u);
}
}
}
}
// no augmenting paths, matching is maximum
return(false);
}