/// <summary>
/// Computes the offline least common ancestor between pairs of vertices in a rooted tree
/// using Tarjan algorithm.
/// </summary>
/// <remarks>
/// Reference:
/// Gabow, H. N. and Tarjan, R. E. 1983. A linear-time algorithm for a special case of disjoint set union. In Proceedings of the Fifteenth Annual ACM Symposium on theory of Computing STOC '83. ACM, New York, NY, 246-251. DOI= http://doi.acm.org/10.1145/800061.808753
/// </remarks>
/// <typeparam name="TVertex">type of the vertices</typeparam>
/// <typeparam name="TEdge">type of the edges</typeparam>
/// <param name="visitedGraph"></param>
/// <param name="root"></param>
/// <param name="pairs"></param>
/// <returns></returns>
public static TryFunc <SEquatableEdge <TVertex>, TVertex> OfflineLeastCommonAncestorTarjan <TVertex, TEdge>(
#if !NET20
this
#endif
IVertexListGraph <TVertex, TEdge> visitedGraph,
TVertex root,
IEnumerable <SEquatableEdge <TVertex> > pairs
)
where TEdge : IEdge <TVertex>
{
Contract.Requires(visitedGraph != null);
Contract.Requires(root != null);
Contract.Requires(pairs != null);
Contract.Requires(visitedGraph.ContainsVertex(root));
Contract.Requires(Enumerable.All(pairs, p => visitedGraph.ContainsVertex(p.Source)));
Contract.Requires(Enumerable.All(pairs, p => visitedGraph.ContainsVertex(p.Target)));
var algo = new TarjanOfflineLeastCommonAncestorAlgorithm <TVertex, TEdge>(visitedGraph);
algo.Compute(root, pairs);
var ancestors = algo.Ancestors;
return(delegate(SEquatableEdge <TVertex> pair, out TVertex value)
{
return ancestors.TryGetValue(pair, out value);
});
}
public static TryFunc <TVertex, IEnumerable <TEdge> > TreeCyclePoppingRandom <TVertex, TEdge>(
#if !NET20
this
#endif
IVertexListGraph <TVertex, TEdge> visitedGraph,
TVertex root,
IMarkovEdgeChain <TVertex, TEdge> edgeChain)
where TEdge : IEdge <TVertex>
{
Contract.Requires(visitedGraph != null);
Contract.Requires(root != null);
Contract.Requires(visitedGraph.ContainsVertex(root));
Contract.Ensures(Contract.Result <TryFunc <TVertex, IEnumerable <TEdge> > >() != null);
var algo = new CyclePoppingRandomTreeAlgorithm <TVertex, TEdge>(visitedGraph, edgeChain);
var predecessorRecorder = new VertexPredecessorRecorderObserver <TVertex, TEdge>();
using (predecessorRecorder.Attach(algo))
algo.Compute(root);
var predecessors = predecessorRecorder.VertexPredecessors;
return(delegate(TVertex v, out IEnumerable <TEdge> edges)
{
return EdgeExtensions.TryGetPath(predecessors, v, out edges);
});
}
public static TryFunc <TVertex, IEnumerable <TEdge> > TreeCyclePoppingRandom <TVertex, TEdge>
(this IVertexListGraph <TVertex, TEdge> visitedGraph, TVertex root)
where TEdge : IEdge <TVertex>
{
Contract.Requires(visitedGraph != null);
Contract.Requires(root != null);
Contract.Requires(visitedGraph.ContainsVertex(root));
Contract.Ensures(Contract.Result <TryFunc <TVertex, IEnumerable <TEdge> > >() != null);
return(TreeCyclePoppingRandom(visitedGraph, root, new NormalizedMarkovEdgeChain <TVertex, TEdge>()));
}
/// <summary>
/// Computes a depth first tree.
/// </summary>
/// <typeparam name="TVertex">The type of the vertex.</typeparam>
/// <typeparam name="TEdge">The type of the edge.</typeparam>
/// <param name="visitedGraph">The visited graph.</param>
/// <param name="root">The root.</param>
/// <returns></returns>
public static TryFunc <TVertex, IEnumerable <TEdge> > TreeDepthFirstSearch <TVertex, TEdge>
(this IVertexListGraph <TVertex, TEdge> visitedGraph, TVertex root)
where TEdge : IEdge <TVertex>
{
Contract.Requires(visitedGraph != null);
Contract.Requires(root != null);
Contract.Requires(visitedGraph.ContainsVertex(root));
Contract.Ensures(Contract.Result <TryFunc <TVertex, IEnumerable <TEdge> > >() != null);
var algo = new DepthFirstSearchAlgorithm <TVertex, TEdge>(visitedGraph);
var predecessorRecorder = new VertexPredecessorRecorderObserver <TVertex, TEdge>();
using (predecessorRecorder.Attach(algo))
algo.Compute(root);
var predecessors = predecessorRecorder.VertexPredecessors;
return(delegate(TVertex v, out IEnumerable <TEdge> edges)
{
return EdgeExtensions.TryGetPath(predecessors, v, out edges);
});
}