public bool IsAdjacentTo(Vertex v, Edge[] edges)
{
var connectingEdges = from e in edges
where e.ConnectedTo(v)
&& e.ConnectedTo(this)
orderby e.Cost
select e;
this.AdjacentEdge = connectingEdges.FirstOrDefault();
return this.AdjacentEdge != null;
}
private static string GetPath(Vertex v)
{
string result = string.Empty;
for (Vertex current = v; current != null; current = current.Parent)
{
if (current.Parent != null)
{
result = string.Format(" - {0}{1}", current.Name, result);
}
else
{
result = current.Name + result;
}
}
return result;
}
private static IEnumerable<Vertex> Dijkstra(
Vertex[] nodes,
Edge[] edges,
Vertex source)
{
source.Cost = 0;
var treeNodes = new List<Vertex>();
var fringe = new List<Vertex>() { source };
for (int i = 0; i < nodes.Length; i++)
{
var remainder = nodes.Where(n => !treeNodes.Contains(n)).ToList();
var u = fringe.OrderBy(n => n.Cost).First();
if (u != source)
{
WritePathTo(u);
}
treeNodes.Add(u);
foreach (var r in remainder)
{
if (r.IsAdjacentTo(u, edges))
{
int c = u.Cost + r.AdjacentEdge.Cost;
if (c < r.Cost)
{
r.Cost = c;
r.Parent = u;
}
if (!fringe.Contains(r))
{
fringe.Add(r);
}
}
}
fringe.Remove(u);
Console.Write("{0}|{1}|{2}", u, string.Join(", ", fringe), null);
}
return treeNodes;
}
public Vertex OtherNode(Vertex that)
{
return Ends.Where(v => v != that).Single();
}
public bool ConnectedTo(Vertex v)
{
return Ends.Any(n => n == v);
}
public Edge(int cost, Vertex v, Vertex u)
{
_Cost = cost;
ends = new[] { v, u };
}
private static void Main()
{
Vertex[] nodes = new Vertex[]
{
new Vertex("a"),
new Vertex("b"),
new Vertex("c"),
new Vertex("d"),
new Vertex("e"),
new Vertex("f"),
new Vertex("g"),
new Vertex("h"),
new Vertex("i"),
new Vertex("j"),
new Vertex("k"),
new Vertex("l"),
};
Edge[] edges = new[]
{
new Edge(3, nodes[0], nodes[1]),
new Edge(5, nodes[0], nodes[2]),
new Edge(4, nodes[0], nodes[3]),
new Edge(3, nodes[1], nodes[4]),
new Edge(6, nodes[1], nodes[5]),
new Edge(2, nodes[2], nodes[3]),
new Edge(1, nodes[3], nodes[4]),
new Edge(2, nodes[4], nodes[5]),
new Edge(4, nodes[2], nodes[6]),
new Edge(5, nodes[3], nodes[7]),
new Edge(4, nodes[4], nodes[8]),
new Edge(5, nodes[5], nodes[9]),
new Edge(3, nodes[6], nodes[7]),
new Edge(6, nodes[7], nodes[8]),
new Edge(3, nodes[8], nodes[9]),
new Edge(6, nodes[6], nodes[10]),
new Edge(7, nodes[7], nodes[10]),
new Edge(5, nodes[8], nodes[11]),
new Edge(9, nodes[9], nodes[11]),
new Edge(8, nodes[10], nodes[11]),
};
Dijkstra(nodes, edges, nodes[0]);
}
private static void WritePathTo(Vertex v)
{
Console.WriteLine(
"to {0}: {1} of length {2}",
v.Name,
GetPath(v),
v.Cost);
}
/// <summary>
/// Create the vertices (this is pretty long)
/// </summary>
public void InstantiateVertexes()
{
Vertex vA = new Vertex("A");
Vertex vB = new Vertex("B");
Vertex vC = new Vertex("C");
Vertex vD = new Vertex("D");
Vertex vE = new Vertex("E");
Vertex vF = new Vertex("F");
Vertex vG = new Vertex("G");
Vertex vH = new Vertex("H");
Vertex vI = new Vertex("I");
Vertex vJ = new Vertex("J");
Vertex vK = new Vertex("K");
Vertex vL = new Vertex("L");
Vertex vM = new Vertex("M");
Vertex vN = new Vertex("N");
Vertex vO = new Vertex("O");
Vertex vP = new Vertex("P");
Vertex vQ = new Vertex("Q");
Vertex vR = new Vertex("R");
Vertex vS = new Vertex("S");
Vertex vT = new Vertex("T");
Vertex vU = new Vertex("U");
Vertex vV = new Vertex("V");
Vertex vW = new Vertex("W");
Vertex vX = new Vertex("X");
Vertex vY = new Vertex("Y");
Vertex vZ = new Vertex("Z");
GraphList.Add(vA);
GraphDictionary.Add("A", vA);
GraphList.Add(vB);
GraphDictionary.Add("B", vB);
GraphList.Add(vC);
GraphDictionary.Add("C", vC);
GraphList.Add(vD);
GraphDictionary.Add("D", vD);
GraphList.Add(vE);
GraphDictionary.Add("E", vE);
GraphList.Add(vF);
GraphDictionary.Add("F", vF);
GraphList.Add(vG);
GraphDictionary.Add("G", vG);
GraphList.Add(vH);
GraphDictionary.Add("H", vH);
GraphList.Add(vI);
GraphDictionary.Add("I", vI);
GraphList.Add(vJ);
GraphDictionary.Add("J", vJ);
GraphList.Add(vK);
GraphDictionary.Add("K", vK);
GraphList.Add(vL);
GraphDictionary.Add("L", vL);
GraphList.Add(vM);
GraphDictionary.Add("M", vM);
GraphList.Add(vN);
GraphDictionary.Add("N", vN);
GraphList.Add(vO);
GraphDictionary.Add("O", vO);
GraphList.Add(vP);
GraphDictionary.Add("P", vP);
GraphList.Add(vQ);
GraphDictionary.Add("Q", vQ);
GraphList.Add(vR);
GraphDictionary.Add("R", vR);
GraphList.Add(vS);
GraphDictionary.Add("S", vS);
GraphList.Add(vT);
GraphDictionary.Add("T", vT);
GraphList.Add(vU);
GraphDictionary.Add("U", vU);
GraphList.Add(vV);
GraphDictionary.Add("V", vV);
GraphList.Add(vW);
GraphDictionary.Add("W", vW);
GraphList.Add(vX);
GraphDictionary.Add("X", vX);
GraphList.Add(vY);
GraphDictionary.Add("Y", vY);
GraphList.Add(vZ);
GraphDictionary.Add("Z", vZ);
}