public ImmutableList <ImmutableHashSet <T> > Solve <T>(IDirectedAcyclicGraph <T> graph)
where T : IEquatable <T>
{
var reducedGraph = DirectedAcyclicGraphTransitiveReducer <T> .ReduceGraph(graph);
return(internalSolver.Solve(reducedGraph));
}
public ImmutableList <ImmutableHashSet <T> > Solve <T>(IDirectedAcyclicGraph <T> graph)
where T : IEquatable <T>
{
if (graph.Count == 0)
{
return(ImmutableList <ImmutableHashSet <T> > .Empty);
}
var ordering = createTopologicalOrdering(graph);
return(createLayers(graph, ordering, maxLayerSize));
}
// ReSharper disable once SuggestBaseTypeForParameter
private static IEnumerable <T> getAllSuccessorsRecursively(IDirectedAcyclicGraph <T> graph, T start)
{
yield return(start);
foreach (var child in graph.GetDirectSuccessorsOf(start))
{
foreach (var descendant in getAllSuccessorsRecursively(graph, child))
{
yield return(descendant);
}
}
}
// ReSharper disable once SuggestBaseTypeForParameter
private static IList <T> createTopologicalOrdering <T>(IDirectedAcyclicGraph <T> graph)
where T : IEquatable <T>
{
// The topological ordering from low to high.
var ordering = new List <T>(graph.Count);
var elements = new HashSet <T>(graph.Elements);
var orderedElementIndices = new Dictionary <T, int>();
while (ordering.Count < graph.Count)
{
// All the remaining elements which have all their predecessors added to the topological ordering
// already. This includes elements which have no predecessors at all. This is equivalent to the set
// of sources in a directed acyclic graph where all already elements and adjacent arrows have been
// removed.
var sources = elements.Where(allPredecessorsHaveBeenOrdered);
// For each considered element, we look at the place of all their predecessors in the partial
// topological ordering we have constructed so far.
// * We first consider the most recently added predecessor of each element. That is, the predecessor
// of said element that is the highest in the current partial topological ordering.
// * Of all these predecessors, we pick the predecessor that is lowest in the ordering. If
// there is only one element with said predecessor, that element is added to the ordering next.
// * Ties are broken by looking at the next highest ordered predecessor of all tied elements.
// * If all predecessors of 2 or more elements are the same, we pick the element with the least
// predecessors.
// This selection process is implemented by representing the predecessors of an element as a
// decreasing number sequence of the predecessors' indices, and selecting the lowest of those in a
// reflected lexicographic ordering.
var next = sources.MinBy(createDecreasingNumberSequenceOfPredecessorIndices);
orderedElementIndices.Add(next, ordering.Count);
ordering.Add(next);
elements.Remove(next);
}
return(ordering);
bool allPredecessorsHaveBeenOrdered(T e) => graph.GetDirectPredecessorsOf(e)
.All(n => orderedElementIndices.ContainsKey(n));
DecreasingNumberSequence createDecreasingNumberSequenceOfPredecessorIndices(T e)
{
var predecessorIndices = graph.GetDirectPredecessorsOf(e).Select(n => orderedElementIndices[n]);
return(DecreasingNumberSequence.FromUnsortedNumbers(predecessorIndices));
}
}
private static ImmutableList <ImmutableHashSet <T> > createLayers <T>(
// ReSharper disable once SuggestBaseTypeForParameter
IDirectedAcyclicGraph <T> graph, IList <T> ordering, int maxLayerSize)
where T : IEquatable <T>
{
var layersReversed = new List <ImmutableHashSet <T> .Builder>();
var elementToLayer = new Dictionary <T, int>();
for (var i = ordering.Count - 1; i >= 0; i--)
{
// We fill in the layers from the last to the first (or bottom to top, if using the traditional
// representation where parents go above their children). For each element, we always choose the
// layer closest to the last (or lowest), such that all its successors are in a later (or lower)
// layer, and the layer has less than W elements.
// The list represents the layers in reverse order, meaning that the last layer of our result is the
// first element in the list. This allows us to use the automatic growing property of the list.
// Combining these two things, the following looks for the lowest integer k such that (1) each
// successor is in a set with an index lower lower than k, and (2) the set at index k has less than
// W elements.
// Requirement (1)
var highestSuccessorLevel = graph.GetDirectSuccessorsOf(ordering[i])
.Select(elmt => elementToLayer[elmt] + 1)
.Aggregate(0, Math.Max);
// Requirement (2)
var candidateLayer = highestSuccessorLevel;
while (
candidateLayer < layersReversed.Count && layersReversed[candidateLayer].Count == maxLayerSize)
{
candidateLayer++;
}
// Expand the list as needed
while (candidateLayer >= layersReversed.Count)
{
layersReversed.Add(ImmutableHashSet.CreateBuilder <T>());
}
// Add the element to the layer
layersReversed[candidateLayer].Add(ordering[i]);
elementToLayer.Add(ordering[i], candidateLayer);
}
return(ImmutableList.CreateRange(layersReversed.Select(b => b.ToImmutable()).Reverse()));
}
public static IDirectedAcyclicGraph <T> ReduceGraph(IDirectedAcyclicGraph <T> graph)
{
var elementsEnumerable = graph.Elements;
var elements = elementsEnumerable as IList <T> ?? elementsEnumerable.ToList();
var graphBuilder = DirectedGraphBuilder <T> .NewBuilder();
foreach (var element in elements)
{
graphBuilder.AddElement(element);
}
foreach (var element in elements)
{
foreach (var child in getOnlyChildrenWithoutIndirectPath(graph, element))
{
graphBuilder.AddArrow(element, child);
}
}
return(graphBuilder.CreateAcyclicGraphUnsafe());
}
private static IEnumerable <T> getOnlyChildrenWithoutIndirectPath(IDirectedAcyclicGraph <T> graph, T element)
{
var childrenEnumerable = graph.GetDirectSuccessorsOf(element);
var children = childrenEnumerable as IList <T>
?? childrenEnumerable.ToList();
var reducedEdges = new HashSet <T>(children);
foreach (var child in children)
{
foreach (var descendant in getAllSuccessorsRecursively(graph, child))
{
if (descendant.Equals(child))
{
continue;
}
// Every arrow to a successor of our direct child is already reachable.
reducedEdges.Remove(descendant);
}
}
return(reducedEdges);
}
