This is a simple mini project to provide two extension methods to group collections by a transitively completed relation.
The already existing GroupBy assumes / only properly works with equivalence relations (i.e. reflexive, symmetric, transitive relations).
A more general (in particular non-transitive) relation can be extended to an equivalence relation by simply (transitively) accumulating all related entries into one group. This can/could be very useful in some situations.
This very implicit GroupBy cannot easily be deduced from existing methods like GroupBy. Hence this mini project.
public static List<List<TSource>> TransitiveGroupBy<TSource>(
this IEnumerable<TSource> source,
Func<TSource, TSource, bool> relation,
IEqualityComparer<TSource>? comparer = null)
where TSource: notnullsource.TransitiveGroupBy(relation) groups the given source (into a list of lists) based on the transitively completed relation.
I.e. two elements are in the same group if and only if there exists a sequence s_{1}, s_{2}, ..., s_{n} with relation(s_{i}, s_{i+1}) = true for all i=1,...,n-1.
The algorithm will internally use the provided comparer to distinguish elements.
If comparer = null (most common case) then the default EqualityComparer for TSource is used.
Remark: It doesn't matter if the relation is reflexive or symmetric (the result will be the same if the relation is made reflexive/symmetric).
public static List<List<TSource>> TransitiveMerge<TSource>(
this IEnumerable<ICollection<TSource>> source,
IEqualityComparer<TSource>? comparer = null)
where TSource : notnullTransitiveMerge(sourceCollectionEnumerable, comparer) merges intersecting lists until they are distinct.
The algorithm will internally use the provided comparer to distinguish elements.
If comparer = null then the default EqualityComparer for TSource is used.
Equal elements will be reduced to one element.
TODO