public void IsBipartite_ForBiggerGraphs()
{
// This graph is some bipartite mess. Odds and evens go in their own set, edges between them haphazardly.
var graph = SimpleGraph.CreateFromOneBasedEdges(22, new[, ]
{
{ 2, 3 }, { 2, 9 }, { 2, 11 }, { 2, 15 },
{ 4, 1 }, { 4, 7 }, { 4, 11 }, { 4, 17 },
{ 6, 1 }, { 6, 11 }, { 6, 7 }, { 6, 15 },
{ 8, 1 }, { 8, 15 }, { 8, 13 }, { 8, 17 },
{ 10, 1 }, { 10, 3 }, { 10, 13 }, { 10, 15 },
{ 14, 1 }, { 16, 3 }, { 16, 7 }, { 16, 17 },
{ 16, 1 }, { 16, 3 }, { 16, 7 }, { 16, 17 },
{ 16, 9 }, { 16, 11 }, { 16, 5 }, { 16, 19 },
{ 18, 9 }, { 18, 11 }, { 18, 5 }, { 18, 19 },
{ 20, 21 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph is like above, except I threw in an edge between an even pair of vertices.
graph = SimpleGraph.CreateFromOneBasedEdges(22, new[, ]
{
{ 2, 3 }, { 2, 9 }, { 2, 11 }, { 2, 15 },
{ 4, 1 }, { 4, 7 }, { 4, 11 }, { 4, 17 },
{ 6, 1 }, { 6, 11 }, { 6, 7 }, { 6, 15 },
{ 8, 1 }, { 8, 15 }, { 8, 13 }, { 8, 17 },
{ 10, 1 }, { 10, 3 }, { 10, 13 }, { 10, 15 },
{ 14, 1 }, { 16, 3 }, { 16, 7 }, { 16, 17 },
{ 16, 1 }, { 16, 3 }, { 16, 7 }, { 16, 17 },
{ 16, 9 }, { 16, 11 }, { 16, 5 }, { 16, 19 },
{ 18, 9 }, { 18, 11 }, { 18, 5 }, { 18, 19 },
{ 20, 21 }, { 10, 16 }
});
Assert.IsFalse(graph.IsBipartite());
}
// Skipping the details, a graph is a tree if it's connected and has (vertexCount - 1) edges.
public static bool Solve(int vertexCount, int edgeCount, int[,] edges)
{
if (edgeCount != vertexCount - 1)
{
return(false);
}
return(SimpleGraph
.CreateFromOneBasedEdges(vertexCount, edges)
.IsConnected());
}
// See image for details: http://i.imgur.com/hWnw1N9.jpg.
public static int Solve(int nodeCount, int[,] edges)
{
if (nodeCount == 1)
{
return(0);
}
var graph = SimpleGraph.CreateFromOneBasedEdges(nodeCount, edges);
var firstVertex = graph.Vertices.First(v => v.Degree == 1);
var secondVertex = graph.FindFurthestVertex(firstVertex).Item1;
int longestPathLength = graph.FindFurthestVertex(secondVertex).Item2;
return(longestPathLength);
}
public void ValidatesAGraph3()
{
var graph = SimpleGraph.CreateFromOneBasedEdges(3, new[, ]
{
{ 1, 2 }, { 2, 3 }
});
Assert.IsTrue(graph.Vertices[0].HasNeighbor(1));
Assert.IsTrue(graph.Vertices[1].HasNeighbor(0));
Assert.IsTrue(graph.Vertices[1].HasNeighbor(2));
Assert.IsTrue(graph.Vertices[2].HasNeighbor(1));
Assert.IsTrue(graph.HasEdge(0, 1));
Assert.IsTrue(graph.HasEdge(1, 2));
Assert.AreEqual(1, graph.Vertices[0].Degree);
Assert.AreEqual(2, graph.Vertices[1].Degree);
Assert.AreEqual(1, graph.Vertices[2].Degree);
}
