public void SetUp()
{
directedGraph = new DirectedSimpleGraph <int, object, object>(Enumerable.Range(0, 10));
directedGraph.AddEdgeBetween(directedGraph[0], directedGraph[1]);
directedGraph.AddEdgeBetween(directedGraph[1], directedGraph[3]);
directedGraph.AddEdgeBetween(directedGraph[1], directedGraph[7]);
directedGraph.AddEdgeBetween(directedGraph[3], directedGraph[4]);
directedGraph.AddEdgeBetween(directedGraph[4], directedGraph[0]);
directedGraph.AddEdgeBetween(directedGraph[5], directedGraph[4]);
directedGraph.AddEdgeBetween(directedGraph[5], directedGraph[8]);
directedGraph.AddEdgeBetween(directedGraph[6], directedGraph[2]);
directedGraph.AddEdgeBetween(directedGraph[6], directedGraph[9]);
directedGraph.AddEdgeBetween(directedGraph[8], directedGraph[5]);
undirectedGraph = new UndirectedSimpleGraph <int, object, object>(Enumerable.Range(0, 10));
undirectedGraph.AddEdgeBetween(undirectedGraph[0], undirectedGraph[1]);
undirectedGraph.AddEdgeBetween(undirectedGraph[0], undirectedGraph[4]);
undirectedGraph.AddEdgeBetween(undirectedGraph[1], undirectedGraph[3]);
undirectedGraph.AddEdgeBetween(undirectedGraph[1], undirectedGraph[7]);
undirectedGraph.AddEdgeBetween(undirectedGraph[2], undirectedGraph[6]);
undirectedGraph.AddEdgeBetween(undirectedGraph[3], undirectedGraph[4]);
undirectedGraph.AddEdgeBetween(undirectedGraph[4], undirectedGraph[5]);
undirectedGraph.AddEdgeBetween(undirectedGraph[5], undirectedGraph[8]);
undirectedGraph.AddEdgeBetween(undirectedGraph[6], undirectedGraph[9]);
}
public void SetUp()
{
graph = new UndirectedSimpleGraph <int, object, WeightProp>(Enumerable.Range(0, 5).ToArray());
graph.AddEdgeBetween(graph[0], graph[1], new WeightProp {
Weight = -1.0
});
graph.AddEdgeBetween(graph[0], graph[2], new WeightProp {
Weight = 4.0
});
graph.AddEdgeBetween(graph[1], graph[2], new WeightProp {
Weight = 9.0
});
graph.AddEdgeBetween(graph[1], graph[3], new WeightProp {
Weight = 7.0
});
graph.AddEdgeBetween(graph[1], graph[4], new WeightProp {
Weight = 12.0
});
graph.AddEdgeBetween(graph[2], graph[4], new WeightProp {
Weight = 6.0
});
graph.AddEdgeBetween(graph[3], graph[4], new WeightProp {
Weight = 3.0
});
}
/// <summary>Kruskal algorithm.</summary>
/// <param name="graph">Undirected weighted graph</param>
/// <returns>Minimal spanning tree</returns>
public static IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> Kruskal <TVertexId, TVertexProperty, TEdgeProperty>(
this IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> graph)
where TEdgeProperty : IWeighted
{
var mst = new UndirectedSimpleGraph <TVertexId, TVertexProperty, TEdgeProperty>(
graph.Vertices.Select(v => v.Id).ToArray());
var vertexSets = new DisjointSets <Vertex <TVertexId> >(graph.Vertices);
var edgeHeap = new Heap <Edge <TVertexId> >(
(edge1, edge2) => graph.Properties[edge1].Weight.CompareTo(graph.Properties[edge2].Weight)
);
foreach (Edge <TVertexId> edge in graph.Edges)
{
edgeHeap.Push(edge);
}
while (vertexSets.Count > 1 && edgeHeap.Count > 0)
{
Edge <TVertexId> edge = edgeHeap.Pop();
if (!vertexSets.IsSameSet(edge.Source, edge.Destination))
{
mst.AddEdge(edge, graph.Properties[edge]);
}
vertexSets.UnionSet(edge.Source, edge.Destination);
}
return(mst);
}
public void FindVertexCut_WhenPresentSeparators_ThenSeparators()
{
// given
var graph = new UndirectedSimpleGraph <int, object, object>(Enumerable.Range(0, 12));
graph.AddEdgeBetween(graph[0], graph[1]);
graph.AddEdgeBetween(graph[0], graph[2]);
graph.AddEdgeBetween(graph[0], graph[7]);
graph.AddEdgeBetween(graph[1], graph[2]);
graph.AddEdgeBetween(graph[1], graph[3]);
graph.AddEdgeBetween(graph[1], graph[4]);
graph.AddEdgeBetween(graph[3], graph[5]);
graph.AddEdgeBetween(graph[4], graph[5]);
graph.AddEdgeBetween(graph[5], graph[6]);
graph.AddEdgeBetween(graph[7], graph[8]);
graph.AddEdgeBetween(graph[7], graph[9]);
graph.AddEdgeBetween(graph[7], graph[11]);
graph.AddEdgeBetween(graph[8], graph[9]);
graph.AddEdgeBetween(graph[9], graph[10]);
graph.AddEdgeBetween(graph[9], graph[11]);
graph.AddEdgeBetween(graph[10], graph[11]);
// when
IEnumerable <Vertex <int> > result = graph.FindVertexCut();
// then
result.Should().BeEquivalentTo(
new[] { graph[0], graph[1], graph[5], graph[7] });
}
/// <summary>Prim algorithm.</summary>
/// <param name="graph">Undirected weighted graph</param>
/// <param name="source">Starting vertex</param>
/// <returns>Minimal spanning tree</returns>
public static IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> Prim <TVertexId, TVertexProperty, TEdgeProperty>(
IUndirectedGraph <TVertexId, TVertexProperty, TEdgeProperty> graph, Vertex <TVertexId> source)
where TEdgeProperty : IWeighted
{
var mst = new UndirectedSimpleGraph <TVertexId, TVertexProperty, TEdgeProperty>(
graph.Vertices.Select(v => v.Id).ToArray());
var visited = new HashSet <Vertex <TVertexId> >();
var heap = new Heap <(Edge <TVertexId>, Vertex <TVertexId>)>(
(pair1, pair2) => graph.Properties[pair1.Item1].Weight.CompareTo(
graph.Properties[pair2.Item1].Weight)
);
visited.Add(source);
foreach (Edge <TVertexId> adjacentEdge in graph.GetAdjacentEdges(source))
{
Vertex <TVertexId> neighbour = adjacentEdge.GetNeighbour(source);
if (neighbour != source)
{
heap.Push((adjacentEdge, neighbour));
}
}
while (heap.Count > 0)
{
(Edge <TVertexId> edge, Vertex <TVertexId> vertex) = heap.Pop();
if (!visited.Contains(vertex))
{
visited.Add(vertex);
mst.AddEdge(edge, graph.Properties[edge]);
foreach (Edge <TVertexId> adjacentEdge in graph.GetAdjacentEdges(vertex))
{
Vertex <TVertexId> neighbour = adjacentEdge.GetNeighbour(vertex);
if (!visited.Contains(neighbour))
{
heap.Push((adjacentEdge, neighbour));
}
}
}
}
return(mst);
}
public void FindEdgeCut_WhenNoBridges_ThenEmptyList()
{
// given
var graph = new UndirectedSimpleGraph <int, object, object>(Enumerable.Range(0, 6));
graph.AddEdgeBetween(graph[0], graph[1]);
graph.AddEdgeBetween(graph[0], graph[2]);
graph.AddEdgeBetween(graph[1], graph[2]);
graph.AddEdgeBetween(graph[1], graph[3]);
graph.AddEdgeBetween(graph[1], graph[4]);
graph.AddEdgeBetween(graph[3], graph[5]);
graph.AddEdgeBetween(graph[4], graph[5]);
// when
IEnumerable <Edge <int> > result = graph.FindEdgeCut();
// then
result.Should().BeEmpty();
}
public void SetUp()
{
directedGraph = new DirectedSimpleGraph <int, object, Weighted>(
Enumerable.Range(0, 10).ToList());
directedGraph.AddEdgeBetween(directedGraph[0], directedGraph[1],
new Weighted(4.0));
directedGraph.AddEdgeBetween(directedGraph[1], directedGraph[4],
new Weighted(7.0));
directedGraph.AddEdgeBetween(directedGraph[1], directedGraph[7],
new Weighted(12.0));
directedGraph.AddEdgeBetween(directedGraph[2], directedGraph[4],
new Weighted(6.0));
directedGraph.AddEdgeBetween(directedGraph[2], directedGraph[6],
new Weighted(8.0));
directedGraph.AddEdgeBetween(directedGraph[3], directedGraph[0],
new Weighted(3.0));
directedGraph.AddEdgeBetween(directedGraph[3], directedGraph[7],
new Weighted(5.0));
directedGraph.AddEdgeBetween(directedGraph[4], directedGraph[5],
new Weighted(1.0));
directedGraph.AddEdgeBetween(directedGraph[4], directedGraph[3],
new Weighted(10.0));
directedGraph.AddEdgeBetween(directedGraph[5], directedGraph[6],
new Weighted(4.0));
directedGraph.AddEdgeBetween(directedGraph[5], directedGraph[8],
new Weighted(2.0));
directedGraph.AddEdgeBetween(directedGraph[6], directedGraph[5],
new Weighted(7.0));
directedGraph.AddEdgeBetween(directedGraph[7], directedGraph[5],
new Weighted(2.0));
directedGraph.AddEdgeBetween(directedGraph[7], directedGraph[8],
new Weighted(6.0));
directedGraph.AddEdgeBetween(directedGraph[8], directedGraph[9],
new Weighted(10.0));
directedGraph.AddEdgeBetween(directedGraph[9], directedGraph[6],
new Weighted(3.0));
undirectedGraph = new UndirectedSimpleGraph <int, object, Weighted>(
Enumerable.Range(0, 10).ToList());
undirectedGraph.AddEdgeBetween(undirectedGraph[0], undirectedGraph[1],
new Weighted(4.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[1], undirectedGraph[4],
new Weighted(7.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[1], undirectedGraph[7],
new Weighted(12.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[2], undirectedGraph[6],
new Weighted(8.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[3], undirectedGraph[0],
new Weighted(3.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[3], undirectedGraph[7],
new Weighted(5.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[4], undirectedGraph[5],
new Weighted(1.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[4], undirectedGraph[3],
new Weighted(10.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[5], undirectedGraph[8],
new Weighted(2.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[7], undirectedGraph[5],
new Weighted(2.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[7], undirectedGraph[8],
new Weighted(6.0));
undirectedGraph.AddEdgeBetween(undirectedGraph[9], undirectedGraph[6],
new Weighted(3.0));
}
