// 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));
}
}
