/// <summary>
/// Enumerates triangles as triples (a, b, array of c), where each element of the list makes a triangle with edge (a,b).
/// </summary>
/// <param name="source">An empty bool stream off of which to base the computation; introducing true starts the computation.</param>
/// <param name="emptyIndex">The un-keyed index built off of the graph.</param>
/// <param name="denseIndex">The int-keyed index built off of the graph.</param>
/// <returns>Stream of triangles represented as triples (a, b, cs) of values c completing triangles (a,b).</returns>
public static Stream <Pair <Pair <int, int>, int[]>, Epoch> Triangles(this Stream <bool, Epoch> source,
Indices.EmptyKeyIndex <int, Pair <int, int> > emptyIndex,
DenseIntKeyIndex <Pair <int, int> > denseIndex)
{
// prefix extenders take prefixes of various types and propose / validate new values.
// each of these extender collections are of prefixes of length 0, 1, 2, respectively.
// the length 1 extender is cheating a bit; it does not validate against G(b, *).
var prefixExtenders0 = new[] { emptyIndex.CreateExtender <bool>() };
var prefixExtenders1 = new[] { denseIndex.CreateExtender((int xA) => xA) };
var prefixExtenders2 = new[] { denseIndex.CreateExtender((Pair <int, int> xAB) => xAB.First),
denseIndex.CreateExtender((Pair <int, int> xAB) => xAB.Second) };
// add new variables one layer at a time. we start with a bool, but discard it asap.
var triangles = source.GenericJoinLayer(prefixExtenders0).Expand().Select(x => x.Second)
.GenericJoinLayer(prefixExtenders1).Expand()
.GenericJoinLayer(prefixExtenders2);
return(triangles);
}
public static Stream <Pair <Pair <Pair <int, int>, int>, int>, Epoch> Flags(this Stream <bool, Epoch> source,
Indices.EmptyKeyIndex <int, Pair <int, int> > emptyIndex,
DenseIntKeyIndex <Pair <int, int> > denseIndex)
{
// prefix extenders take prefixes of various types and propose / validate new values.
var prefixExtenders0 = new[] { emptyIndex.CreateExtender <bool>() };
var prefixExtenders1 = new[] { denseIndex.CreateExtender((int xA) => xA) };
var prefixExtenders2 = new[] { denseIndex.CreateExtender((Pair <int, int> xAB) => xAB.First),
denseIndex.CreateExtender((Pair <int, int> xAB) => xAB.Second) };
var prefixExtenders3 = new[] { denseIndex.CreateExtender((Pair <Pair <int, int>, int> xABC) => xABC.First.Second),
denseIndex.CreateExtender((Pair <Pair <int, int>, int> xABC) => xABC.Second) };
// add new variables one layer at a time. we start with a bool, but discard it asap.
var flags = source.GenericJoinLayer(prefixExtenders0).Expand().Select(x => x.Second)
.GenericJoinLayer(prefixExtenders1).Expand()
.GenericJoinLayer(prefixExtenders2).Expand()
.GenericJoinLayer(prefixExtenders3).Expand().Where(x => x.First.First.First != x.Second);
return(flags);
}
