/// <summary>
/// An edge was found which connects two 'even' vertices in the forest. If
/// the vertices have the same root we have a blossom otherwise we have
/// identified an augmenting path. This method checks for these cases and
/// responds accordingly.
/// <para>
/// If an augmenting path was found - then it's edges are alternated and the
/// method returns true. Otherwise if a blossom was found - it is contracted
/// and the search continues.
/// </para>
/// </summary>
/// <param name="v">endpoint of an edge</param>
/// <param name="w">another endpoint of an edge</param>
/// <returns>a path was augmented</returns>
private bool Check(int v, int w)
{
// self-loop (within blossom) ignored
if (uf.Connected(v, w))
{
return(false);
}
vAncestors.SetAll(false);
wAncestors.SetAll(false);
int vCurr = v;
int wCurr = w;
// walk back along the trees filling up 'vAncestors' and 'wAncestors'
// with the vertices in the tree - vCurr and wCurr are the 'even' parents
// from v/w along the tree
while (true)
{
vCurr = Parent(vAncestors, vCurr);
wCurr = Parent(wAncestors, wCurr);
// v and w lead to the same root - we have found a blossom. We
// travelled all the way down the tree thus vCurr (and wCurr) are
// the base of the blossom
if (vCurr == wCurr)
{
Blossom(v, w, vCurr);
return(false);
}
// we are at the root of each tree and the roots are different, we
// have found and augmenting path
if (uf.Find(even[vCurr]) == vCurr && uf.Find(even[wCurr]) == wCurr)
{
Augment(v);
Augment(w);
matching.Match(v, w);
return(true);
}
// the current vertex in 'v' can be found in w's ancestors they must
// share a root - we have found a blossom whose base is 'vCurr'
if (wAncestors[vCurr])
{
Blossom(v, w, vCurr);
return(false);
}
// the current vertex in 'w' can be found in v's ancestors they must
// share a root, we have found a blossom whose base is 'wCurr'
if (vAncestors[wCurr])
{
Blossom(v, w, wCurr);
return(false);
}
}
}
public void Connected()
{
UnionFind uf = new UnionFind(100);
uf.Union(1, 5);
uf.Union(7, 9);
uf.Union(7, 5);
uf.Union(10, 11);
uf.Union(11, 50);
uf.Union(15, 1);
uf.Union(15, 50);
Assert.IsTrue(uf.Connected(1, 5));
Assert.IsTrue(uf.Connected(1, 7));
Assert.IsTrue(uf.Connected(1, 9));
Assert.IsTrue(uf.Connected(1, 10));
Assert.IsTrue(uf.Connected(1, 11));
Assert.IsTrue(uf.Connected(1, 15));
Assert.IsTrue(uf.Connected(1, 50));
}