public void ForestCyclesCheck()
{
var vertices = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 };
var graph = new WeightedALGraph <int, int>();
graph.AddVertices(vertices);
// Graph is:
// first component
// 1 <-> 2, 3, 4
// 2 <-> 1, 3, 5, 6
// 3 <-> 1, 2, 6
// 4 <-> 1, 6, 7
// 5 <-> 2, 7, 8
// 6 <-> 2, 3, 4
// 7 <-> 4, 8
// 8 <-> 7, 5
// second component
// 9 <-> 10, 12
// 10 <-> 9, 11, 12
// 11 <-> 10, 12, 13
// 12 <-> 9, 10, 11
// 13 <-> 11
// third component
// 14 <-> 15, 16
// 15 <-> 14, 16
// 16 <-> 14, 15
// With each edge having a weight of the absolute value of the difference of the vertices
graph.AddEdge(1, 2, 1);
graph.AddEdge(1, 3, 2);
graph.AddEdge(1, 4, 3);
graph.AddEdge(2, 3, 1);
graph.AddEdge(2, 5, 3);
graph.AddEdge(2, 6, 4);
graph.AddEdge(3, 6, 3);
graph.AddEdge(4, 6, 2);
graph.AddEdge(4, 7, 3);
graph.AddEdge(5, 7, 2);
graph.AddEdge(5, 8, 3);
graph.AddEdge(7, 8, 1);
graph.AddEdge(9, 10, 1);
graph.AddEdge(9, 12, 3);
graph.AddEdge(10, 11, 1);
graph.AddEdge(10, 12, 2);
graph.AddEdge(11, 12, 1);
graph.AddEdge(11, 13, 2);
graph.AddEdge(14, 15, 1);
graph.AddEdge(14, 16, 2);
graph.AddEdge(15, 16, 1);
// Graph has to be cyclic
Assert.IsTrue(graph.IsCyclic());
// Compute MST of the graph
var mst = graph.KruskalMST();
// The MST is acyclic
Assert.IsFalse(mst.IsCyclic());
}
public void StringWeightsMST()
{
var vertices = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
var graph = new WeightedALGraph <int, string>();
graph.AddVertices(vertices);
// Graph is:
// 1 <-> 2, 3, 4
// 2 <-> 1, 3, 5, 6
// 3 <-> 1, 2, 6
// 4 <-> 1, 6, 7
// 5 <-> 2, 7, 8
// 6 <-> 2, 3, 4
// 7 <-> 4, 8
// 8 <-> 7, 5
// 9 <->
graph.AddEdge(1, 2, "a");
graph.AddEdge(1, 3, "b");
graph.AddEdge(1, 4, "b");
graph.AddEdge(2, 3, "a");
graph.AddEdge(2, 5, "c");
graph.AddEdge(2, 6, "c");
graph.AddEdge(3, 6, "c");
graph.AddEdge(4, 6, "b");
graph.AddEdge(4, 7, "b");
graph.AddEdge(5, 7, "b");
graph.AddEdge(5, 8, "c");
graph.AddEdge(7, 8, "a");
// Expected MST
// 1 <-> 2, 4
// 2 <-> 3
// 3 <-> 2
// 4 <-> 1, 6, 7
// 5 <-> 7
// 6 <-> 4
// 7 <-> 4, 5, 8
// 8 <-> 7
// 9 <->
var mst = graph.KruskalMST();
string weight = string.Empty;
Assert.IsTrue(mst.TryGetEdgeWeight(1, 2, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsTrue(mst.TryGetEdgeWeight(2, 1, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsTrue(mst.TryGetEdgeWeight(1, 4, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(4, 1, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(2, 3, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsTrue(mst.TryGetEdgeWeight(3, 2, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsTrue(mst.TryGetEdgeWeight(4, 6, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(6, 4, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(4, 7, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(7, 4, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(5, 7, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(7, 5, out weight));
Assert.IsTrue(object.Equals(weight, "b"));
Assert.IsTrue(mst.TryGetEdgeWeight(7, 8, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsTrue(mst.TryGetEdgeWeight(8, 7, out weight));
Assert.IsTrue(object.Equals(weight, "a"));
Assert.IsFalse(mst.ContainsEdge(1, 3));
Assert.IsFalse(mst.ContainsEdge(3, 1));
Assert.IsFalse(mst.ContainsEdge(2, 5));
Assert.IsFalse(mst.ContainsEdge(5, 2));
Assert.IsFalse(mst.ContainsEdge(2, 6));
Assert.IsFalse(mst.ContainsEdge(6, 2));
Assert.IsFalse(mst.ContainsEdge(3, 6));
Assert.IsFalse(mst.ContainsEdge(6, 3));
Assert.IsFalse(mst.ContainsEdge(5, 8));
Assert.IsFalse(mst.ContainsEdge(8, 5));
}
public void MinimumSpanningForest()
{
var vertices = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 };
var graph = new WeightedALGraph <int, int>();
graph.AddVertices(vertices);
// Graph is:
// first component
// 1 <-> 2, 3, 4
// 2 <-> 1, 3, 5, 6
// 3 <-> 1, 2, 6
// 4 <-> 1, 6, 7
// 5 <-> 2, 7, 8
// 6 <-> 2, 3, 4
// 7 <-> 4, 8
// 8 <-> 7, 5
// second component
// 9 <-> 10, 12
// 10 <-> 9, 11, 12
// 11 <-> 10, 12, 13
// 12 <-> 9, 10, 11
// 13 <-> 11
// third component
// 14 <-> 15, 16
// 15 <-> 14, 16
// 16 <-> 14, 15
// With each edge having a weight of the absolute value of the difference of the vertices
graph.AddEdge(1, 2, 1);
graph.AddEdge(1, 3, 2);
graph.AddEdge(1, 4, 3);
graph.AddEdge(2, 3, 1);
graph.AddEdge(2, 5, 3);
graph.AddEdge(2, 6, 4);
graph.AddEdge(3, 6, 3);
graph.AddEdge(4, 6, 2);
graph.AddEdge(4, 7, 3);
graph.AddEdge(5, 7, 2);
graph.AddEdge(5, 8, 3);
graph.AddEdge(7, 8, 1);
graph.AddEdge(9, 10, 1);
graph.AddEdge(9, 12, 3);
graph.AddEdge(10, 11, 1);
graph.AddEdge(10, 12, 2);
graph.AddEdge(11, 12, 1);
graph.AddEdge(11, 13, 2);
graph.AddEdge(14, 15, 1);
graph.AddEdge(14, 16, 2);
graph.AddEdge(15, 16, 1);
// Expected MST
// first component
// 1 <-> 2, 4
// 2 <-> 1, 3, 5
// 3 <-> 2
// 4 <-> 1, 6
// 5 <-> 2, 7
// 6 <-> 4
// 7 <-> 5, 8
// 8 <-> 7
// second component
// 9 <-> 10
// 10 <-> 9, 11
// 11 <-> 10, 12, 13
// 12 <-> 11
// 13 <-> 11
// third component
// 14 <-> 15
// 15 <-> 14, 16
// 16 <-> 15
var mst = graph.KruskalMST();
int weight = 0;
// first component
Assert.IsTrue(mst.TryGetEdgeWeight(1, 2, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(2, 1, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(1, 4, out weight));
Assert.IsTrue(weight == 3);
Assert.IsTrue(mst.TryGetEdgeWeight(4, 1, out weight));
Assert.IsTrue(weight == 3);
Assert.IsTrue(mst.TryGetEdgeWeight(2, 3, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(3, 2, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(2, 5, out weight));
Assert.IsTrue(weight == 3);
Assert.IsTrue(mst.TryGetEdgeWeight(5, 2, out weight));
Assert.IsTrue(weight == 3);
Assert.IsTrue(mst.TryGetEdgeWeight(4, 6, out weight));
Assert.IsTrue(weight == 2);
Assert.IsTrue(mst.TryGetEdgeWeight(6, 4, out weight));
Assert.IsTrue(weight == 2);
Assert.IsTrue(mst.TryGetEdgeWeight(5, 7, out weight));
Assert.IsTrue(weight == 2);
Assert.IsTrue(mst.TryGetEdgeWeight(7, 5, out weight));
Assert.IsTrue(weight == 2);
Assert.IsTrue(mst.TryGetEdgeWeight(7, 8, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(8, 7, out weight));
Assert.IsTrue(weight == 1);
// second component
Assert.IsTrue(mst.TryGetEdgeWeight(9, 10, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(10, 9, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(10, 11, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(11, 10, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(11, 12, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(12, 11, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(11, 13, out weight));
Assert.IsTrue(weight == 2);
Assert.IsTrue(mst.TryGetEdgeWeight(13, 11, out weight));
Assert.IsTrue(weight == 2);
// third component
Assert.IsTrue(mst.TryGetEdgeWeight(14, 15, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(15, 14, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(15, 16, out weight));
Assert.IsTrue(weight == 1);
Assert.IsTrue(mst.TryGetEdgeWeight(16, 15, out weight));
Assert.IsTrue(weight == 1);
// first component
Assert.IsFalse(mst.ContainsEdge(1, 3));
Assert.IsFalse(mst.ContainsEdge(3, 1));
Assert.IsFalse(mst.ContainsEdge(2, 6));
Assert.IsFalse(mst.ContainsEdge(6, 2));
Assert.IsFalse(mst.ContainsEdge(3, 6));
Assert.IsFalse(mst.ContainsEdge(6, 3));
Assert.IsFalse(mst.ContainsEdge(4, 7));
Assert.IsFalse(mst.ContainsEdge(7, 4));
Assert.IsFalse(mst.ContainsEdge(5, 8));
Assert.IsFalse(mst.ContainsEdge(8, 5));
// second component
Assert.IsFalse(mst.ContainsEdge(9, 12));
Assert.IsFalse(mst.ContainsEdge(12, 9));
Assert.IsFalse(mst.ContainsEdge(10, 12));
Assert.IsFalse(mst.ContainsEdge(12, 10));
// third component
Assert.IsFalse(mst.ContainsEdge(14, 16));
Assert.IsFalse(mst.ContainsEdge(16, 14));
}
public void NegativeEdgesWeightsAsVertexDifference()
{
var vertices = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
var graph = new WeightedALGraph <int, int>();
graph.AddVertices(vertices);
// Graph is:
// 1 <-> 2, 3, 4
// 2 <-> 1, 3, 5, 6
// 3 <-> 1, 2, 6
// 4 <-> 1, 6, 7
// 5 <-> 2, 7, 8
// 6 <-> 2, 3, 4
// 7 <-> 4, 8
// 8 <-> 7, 5
// 9 <->
// With each edge having a weight of the absolute value of the difference of the vertices
graph.AddEdge(1, 2, -1);
graph.AddEdge(1, 3, -2);
graph.AddEdge(1, 4, -3);
graph.AddEdge(2, 3, -1);
graph.AddEdge(2, 5, -3);
graph.AddEdge(2, 6, -4);
graph.AddEdge(3, 6, -3);
graph.AddEdge(4, 6, -2);
graph.AddEdge(4, 7, -3);
graph.AddEdge(5, 7, -2);
graph.AddEdge(5, 8, -3);
graph.AddEdge(7, 8, -1);
// Expected MST
// 1 <-> 3, 4
// 2 <-> 5, 6
// 3 <-> 1, 6
// 4 <-> 1, 7
// 5 <-> 2, 8
// 6 <-> 2, 3
// 7 <-> 4
// 8 <-> 5
// 9 <->
var mst = graph.KruskalMST();
int weight = 0;
Assert.IsTrue(mst.TryGetEdgeWeight(1, 3, out weight));
Assert.IsTrue(weight == -2);
Assert.IsTrue(mst.TryGetEdgeWeight(3, 1, out weight));
Assert.IsTrue(weight == -2);
Assert.IsTrue(mst.TryGetEdgeWeight(1, 4, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(4, 1, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(2, 5, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(5, 2, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(2, 6, out weight));
Assert.IsTrue(weight == -4);
Assert.IsTrue(mst.TryGetEdgeWeight(6, 2, out weight));
Assert.IsTrue(weight == -4);
Assert.IsTrue(mst.TryGetEdgeWeight(3, 6, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(6, 3, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(4, 7, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(7, 4, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(5, 8, out weight));
Assert.IsTrue(weight == -3);
Assert.IsTrue(mst.TryGetEdgeWeight(8, 5, out weight));
Assert.IsTrue(weight == -3);
Assert.IsFalse(mst.ContainsEdge(1, 2));
Assert.IsFalse(mst.ContainsEdge(2, 1));
Assert.IsFalse(mst.ContainsEdge(2, 3));
Assert.IsFalse(mst.ContainsEdge(3, 2));
Assert.IsFalse(mst.ContainsEdge(4, 6));
Assert.IsFalse(mst.ContainsEdge(6, 4));
Assert.IsFalse(mst.ContainsEdge(5, 7));
Assert.IsFalse(mst.ContainsEdge(7, 5));
Assert.IsFalse(mst.ContainsEdge(7, 8));
Assert.IsFalse(mst.ContainsEdge(8, 7));
}