/// <summary>
/// Attempt to augment the matching such that it is perfect over the subset
/// of vertices in the provided graph.
/// </summary>
/// <param name="graph">adjacency list representation of graph</param>
/// <param name="subset">subset of vertices</param>
/// <returns>the matching was perfect</returns>
/// <exception cref="ArgumentException">the graph was a different size to the matching capacity</exception>
public bool Perfect(int[][] graph, BitArray subset)
{
if (graph.Length != match.Length || BitArrays.Cardinality(subset) > graph.Length)
{
throw new ArgumentException("graph and matching had different capacity");
}
// and odd set can never provide a perfect matching
if ((BitArrays.Cardinality(subset) & 0x1) == 0x1)
{
return(false);
}
// arbitrary matching was perfect
if (ArbitaryMatching(graph, subset))
{
return(true);
}
EdmondsMaximumMatching.Maxamise(this, graph, subset);
// the matching is imperfect if any vertex was
for (int v = BitArrays.NextSetBit(subset, 0); v >= 0; v = BitArrays.NextSetBit(subset, v + 1))
{
if (Unmatched(v))
{
return(false);
}
}
return(true);
}
private Matching CreateMatching(IAtomContainer container, params int[] xs)
{
BitArray subset = new BitArray(container.Atoms.Count);
if (xs.Length == 0)
{
BitArrays.Flip(subset, 0, container.Atoms.Count);
}
else
{
foreach (var x in xs)
{
subset.Set(x, true);
}
}
Matching m = Matching.WithCapacity(container.Atoms.Count);
return(EdmondsMaximumMatching.Maxamise(m, GraphUtil.ToAdjList(container), subset));
}
