/// <summary>
/// Finds the shortest, weighted path between two vertices, if one exists. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The start of the path.</param>
/// <param name="to">The end of the path.</param>
/// <param name="path">The path that was found. <code>null</code> if there is no path.</param>
/// <returns><code>true</code> if there is a path; <code>false</code> otherwise.</returns>
public bool Dijkstra(uint from, uint to, out Path path)
{
path = null;
DMinHeap<int, uint> fringe = new DMinHeap<int, uint>();
Dictionary<uint, uint> parents = new Dictionary<uint, uint>();
Dictionary<uint, int> dist = new Dictionary<uint, int>();
this.DijkstraInit(from, dist, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
if (current == to)
{
path = Path.FromParents(from, to, parents, this);
return true;
}
this.DijkstraRelax(current, dist, parents, fringe);
}
return false;
}
private void DijkstraInit(uint from, Dictionary<uint, int> dist, DMinHeap<int, uint> fringe)
{
foreach (uint v in this.Vertices.Keys)
{
if (v == from)
dist[v] = 0;
else
dist[v] = int.MaxValue;
fringe.Add(v, dist[v]);
}
}
/// <summary>
/// Find the shortest, weighted paths from a given vertex to all other vertices. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The vertex to calculate the shortest paths from.</param>
/// <param name="lengths">The lengths of the shortest paths to all vertices.</param>
/// <param name="parents">The parent-pointers for the paths to all vertices.</param>
public void Dijkstra(uint from, out Dictionary<uint, int> lengths, out Dictionary<uint, uint> parents)
{
DMinHeap<int, uint> fringe = new DMinHeap<int, uint>();
parents = new Dictionary<uint, uint>();
lengths = new Dictionary<uint, int>();
this.DijkstraInit(from, lengths, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
this.DijkstraRelax(current, lengths, parents, fringe);
}
}
private void DijkstraRelax(uint current, Dictionary<uint, int> dist, Dictionary<uint, uint> parents, DMinHeap<int, uint> fringe)
{
foreach (Edge e in this.Vertices[current].Neighbours.Values)
{
if (!fringe.ContainsValue(e.To))
continue;
int newDist = dist[current] + e.Weight;
if (newDist < dist[e.To])
{
dist[e.To] = newDist;
parents[e.To] = current;
fringe.ChangeKey(e.To, newDist);
}
}
}
