public static Graph GenerateKekuleForm(Graph g, BitArray subset, BitArray aromatic, bool inplace)
{
// make initial (empty) matching - then improve it, first
// by matching the first edges we find, most of time this
// gives us a perfect matching if not we maximise it
// with Edmonds' algorithm
Matching m = Matching.CreateEmpty(g);
int n = BitArrays.Cardinality(subset);
int nMatched = ArbitraryMatching.Initial(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 InvalidSmilesException("Could not Kekulise");
}
}
return(inplace ? Assign(g, subset, aromatic, m)
: CopyAndAssign(g, subset, aromatic, m));
}
/// <summary>Contrived example to test blossoming.</summary>
[TestMethod()] public void Blossom()
{
Graph g = Graph.FromSmiles("CCCCCC1CCCC1CC");
Matching m = Matching.CreateEmpty(g);
// initial matching from double-bonds (size = 5)
m.Match(1, 2);
m.Match(3, 4);
m.Match(5, 6);
m.Match(7, 8);
m.Match(9, 10);
MaximumMatching.Maximise(g, m, 10);
// once maximised the matching has been augmented such that there
// are now six disjoint edges (only possibly by contracting blossom)
Assert.AreEqual(6, m.GetMatches().Count());
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] {
Tuple.Of(0, 1),
Tuple.Of(2, 3),
Tuple.Of(4, 5),
Tuple.Of(6, 7),
Tuple.Of(8, 9),
Tuple.Of(10, 11),
},
m.GetMatches()));
}
public void Simple_maximal()
{
Graph g = Graph.FromSmiles("cccc");
Matching m = MaximumMatching.Maximal(g);
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] { Tuple.Of(0, 1), Tuple.Of(2, 3) },
m.GetMatches()));
}
public void Furan()
{
Graph g = Graph.FromSmiles("o1cccc1");
IntSet s = IntSet.AllOf(1, 2, 3, 4); // exclude the oxygen
Matching m = Matching.CreateEmpty(g);
MaximumMatching.Maximise(g, m, 0, s);
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] { Tuple.Of(1, 2), Tuple.Of(3, 4) },
m.GetMatches()));
}
[TestMethod()] public void Simple_augment()
{
Graph g = Graph.FromSmiles("cccc");
Matching m = Matching.CreateEmpty(g);
m.Match(1, 2);
MaximumMatching.Maximise(g, m, 2);
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] { Tuple.Of(0, 1), Tuple.Of(2, 3) },
m.GetMatches()));
}
[TestMethod()] public void Simple_augment_subset()
{
Graph g = Graph.FromSmiles("cccc");
Matching m = Matching.CreateEmpty(g);
m.Match(1, 2);
// no vertex '3' matching can not be improved
MaximumMatching.Maximise(g, m, 2, IntSet.AllOf(0, 1, 2));
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] { Tuple.Of(1, 2) },
m.GetMatches()));
}
[TestMethod()] public void Imidazole()
{
Graph g = Graph.FromSmiles("[nH]1ccnc1");
Matching m = Matching.CreateEmpty(g);
MaximumMatching.Maximise(g,
m,
0,
IntSet.AllOf(1, 2, 3, 4)); // not the 'nH'
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] { Tuple.Of(1, 2), Tuple.Of(3, 4) },
m.GetMatches()));
}
[TestMethod()] public void Quinone()
{
Graph g = Graph.FromSmiles("Oc1ccc(o)cc1");
Matching m = MaximumMatching.Maximal(g);
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] {
Tuple.Of(0, 1),
Tuple.Of(2, 3),
Tuple.Of(4, 5),
Tuple.Of(6, 7),
},
m.GetMatches()));
}
public void Quinone_subset()
{
Graph g = Graph.FromSmiles("Oc1ccc(o)cc1");
// mocks the case where the oxygen atoms are already double bonded - we
// therefore don't include those of the adjacent carbons in the vertex
// subset to be matched
Matching m = Matching.CreateEmpty(g);
MaximumMatching.Maximise(g, m, 0, IntSet.AllOf(2, 3, 6, 7));
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] {
Tuple.Of(2, 3),
Tuple.Of(6, 7),
},
m.GetMatches()));
}
[TestMethod()] public void Benzimidazole()
{
Graph g = Graph.FromSmiles("c1nc2ccccc2[nH]1");
Matching m = Matching.CreateEmpty(g);
MaximumMatching.Maximise(g,
m,
0,
IntSet.NoneOf(8)); // not the 'nH'
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] {
Tuple.Of(0, 1),
Tuple.Of(2, 3),
Tuple.Of(4, 5),
Tuple.Of(6, 7),
},
m.GetMatches()));
}
public void Napthalene_augment()
{
Graph g = Graph.FromSmiles("C1C=CC2=CCC=CC2=C1");
Matching m = Matching.CreateEmpty(g);
m.Match(1, 2);
m.Match(3, 4);
m.Match(6, 7);
m.Match(8, 9);
MaximumMatching.Maximise(g, m, 8);
Assert.IsTrue(Compares.AreOrderLessDeepEqual(
new[] {
Tuple.Of(0, 1),
Tuple.Of(2, 3),
Tuple.Of(4, 5),
Tuple.Of(6, 7),
Tuple.Of(8, 9),
},
m.GetMatches()));
}
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);
}
/// <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);
}