public static int Dfs(Graph g, Matching m, BitArray s)
{
int nMatched = 0;
BitArray unvisited = (BitArray)s.Clone();
// visit those with degree 1 first and expand out matching
for (int v = BitArrays.NextSetBit(unvisited, 0); v >= 0; v = BitArrays.NextSetBit(unvisited, v + 1))
{
if (!m.Matched(v))
{
int cnt = 0;
int d = g.Degree(v);
while (--d >= 0)
{
int w = g.EdgeAt(v, d).Other(v);
if (unvisited[w])
{
++cnt;
}
}
if (cnt == 1)
{
nMatched += DfsVisit(g, v, m, unvisited, true);
}
}
}
// now those which aren't degree 1
for (int v = BitArrays.NextSetBit(unvisited, 0); v >= 0; v = BitArrays.NextSetBit(unvisited, v + 1))
{
if (!m.Matched(v))
{
nMatched += DfsVisit(g, v, m, unvisited, true);
}
}
return(nMatched);
}
public static int DfsVisit(Graph g, int v, Matching m, BitArray unvisited, bool match)
{
unvisited.Set(v, false);
int nMatched = 0;
int d = g.Degree(v);
while (--d >= 0)
{
int w = g.EdgeAt(v, d).Other(v);
if (unvisited[w])
{
if (match)
{
m.Match(v, w);
return(2 + DfsVisit(g, w, m, unvisited, false));
}
else
{
nMatched += DfsVisit(g, w, m, unvisited, true);
}
}
}
return(nMatched);
}
// invariant, m is a perfect matching
private static Graph CopyAndAssign(Graph delocalised, BitArray subset, BitArray aromatic, Matching m)
{
Graph localised = new Graph(delocalised.Order);
localised.SetFlags(delocalised.GetFlags() & ~Graph.HAS_AROM);
for (int u = 0; u < delocalised.Order; u++)
{
localised.AddAtom(delocalised.GetAtom(u).AsAliphaticForm());
localised.AddTopology(delocalised.TopologyOf(u));
int d = delocalised.Degree(u);
for (int j = 0; j < d; ++j)
{
Edge e = delocalised.EdgeAt(u, j);
int v = e.Other(u);
if (v < u)
{
var aa = e.Bond;
if (aa == Bond.Single)
{
if (aromatic[u] && aromatic[v])
{
localised.AddEdge(Bond.Single.CreateEdge(u, v));
}
else
{
localised.AddEdge(Bond.Implicit.CreateEdge(u, v));
}
}
else if (aa == Bond.Aromatic)
{
if (subset[u] && m.Other(u) == v)
{
localised.AddEdge(Bond.DoubleAromatic.CreateEdge(u, v));
}
else if (aromatic[u] && aromatic[v])
{
localised.AddEdge(Bond.ImplicitAromatic.CreateEdge(u, v));
}
else
{
localised.AddEdge(Bond.Implicit.CreateEdge(u, v));
}
}
else if (aa == Bond.Implicit)
{
if (subset[u] && m.Other(u) == v)
{
localised.AddEdge(Bond.DoubleAromatic.CreateEdge(u, v));
}
else if (aromatic[u] && aromatic[v])
{
localised.AddEdge(Bond.ImplicitAromatic.CreateEdge(u, v));
}
else
{
localised.AddEdge(e);
}
}
else
{
localised.AddEdge(e);
}
}
}
}
return(localised);
}
public static Graph Resonate(Graph g, BitArray cyclic, bool ordered)
{
BitArray subset = new BitArray(g.Order);
for (int u = BitArrays.NextSetBit(cyclic, 0); u >= 0; u = BitArrays.NextSetBit(cyclic, u + 1))
{
// candidates must have a bonded
// valence of one more than their degree
// and in a ring
int uExtra = g.BondedValence(u) - g.Degree(u);
if (uExtra > 0)
{
int other = -1;
Edge target = null;
int d = g.Degree(u);
for (int j = 0; j < d; ++j)
{
Edge e = g.EdgeAt(u, j);
int v = e.Other(u);
// check for bond validity
if (e.Bond.Order == 2)
{
int vExtra = g.BondedValence(v) - g.Degree(v);
if (cyclic[v] && vExtra > 0)
{
if (HasAdjDirectionalLabels(g, e, cyclic) && !InSmallRing(g, e))
{
other = -1;
break;
}
if (vExtra > 1 && HasAdditionalCyclicDoubleBond(g, cyclic, u, v))
{
other = -1;
break;
}
if (other == -1)
{
other = v; // first one
target = e;
}
else
{
other = -2; // found more than one
}
}
// only one double bond don't check any more
if (uExtra == 1)
{
break;
}
}
}
if (other >= 0)
{
subset.Set(u, true);
subset.Set(other, true);
target.SetBond(Bond.Implicit);
}
}
}
if (!ordered)
{
g = g.Sort(new Graph.CanOrderFirst());
}
Matching m = Matching.CreateEmpty(g);
int n = BitArrays.Cardinality(subset);
int nMatched = ArbitraryMatching.Dfs(g, m, subset);
if (nMatched < n)
{
if (n - nMatched == 2)
{
nMatched = ArbitraryMatching.AugmentOnce(g, m, nMatched, subset);
}
if (nMatched < n)
{
nMatched = MaximumMatching.Maximise(g, m, nMatched, IntSet.FromBitArray(subset));
}
if (nMatched < n)
{
throw new ApplicationException("Could not Kekulise");
}
}
// assign new double bonds
for (int v = BitArrays.NextSetBit(subset, 0); v >= 0; v = BitArrays.NextSetBit(subset, v + 1))
{
int w = m.Other(v);
subset.Set(w, false);
g.CreateEdge(v, w).SetBond(Bond.Double);
}
return(g);
}
[TestMethod()] public void IsEmptyTest()
{
Matching matching = Matching.CreateEmpty(Graph.FromSmiles("CCCCC"));
Assert.AreEqual(0, matching.GetMatches().Count());
}
public static int FindPath(Graph g, int v, int end, BitArray unvisited, int[] path, int len, Matching m, bool matchNeeded)
{
unvisited.Set(v, false);
path[len++] = v;
int l;
int d = g.Degree(v);
for (int j = 0; j < d; ++j)
{
Edge e = g.EdgeAt(v, j);
// explicit single bond can not be augmented along!!
if (e.Bond == Bond.Single)
{
continue;
}
int w = e.Other(v);
if (unvisited[w])
{
if (w == end)
{
path[len] = w;
len++;
unvisited.Set(v, true);
// odd length path no good
return(((len & 0x1) == 1) ? 0 : len);
}
else if ((m.Other(w) == v) == matchNeeded)
{
if ((l = FindPath(g, w, end, unvisited, path, len, m, !matchNeeded)) > 0)
{
unvisited.Set(v, true);
return(l);
}
}
}
}
unvisited.Set(v, true);
return(0);
}
/// <summary>
/// Utility to maximise an existing matching of the provided graph.
/// </summary>
/// <param name="g">a graph</param>
/// <param name="m">matching on the graph</param>
/// <param name="n"></param>
/// <returns>the maximal matching on the graph</returns>
public static int Maximise(Graph g, Matching m, int n)
{
return(Maximise(g, m, n, IntSet.Universe));
}
/// <summary>
/// Utility to maximise an existing matching of the provided graph.
/// </summary>
/// <param name="g">a graph</param>
/// <param name="m">matching on the graph, will me modified</param>
/// <param name="n">current matching cardinality</param>
/// <param name="s">subset of vertices to match</param>
/// <returns>the maximal matching on the graph</returns>
public static int Maximise(Graph g, Matching m, int n, IntSet s)
{
MaximumMatching mm = new MaximumMatching(g, m, n, s);
return(mm.nMatched);
}