// TODO: This method should be private and should be called from the bottom of the constructor
/// <summary>
/// check optimality conditions:
/// </summary>
/// <param name="graph">The edge-weighted directed graph</param>
/// <param name="sourceVertex">The source vertex to check optimality conditions from</param>
/// <returns>True if all optimality conditions are met, false otherwise</returns>
/// <exception cref="ArgumentNullException">Thrown on null EdgeWeightedDigraph</exception>
public bool Check(EdgeWeightedDigraph graph, int sourceVertex)
{
if (graph == null)
{
throw new ArgumentNullException("graph", "EdgeWeightedDigraph cannot be null");
}
if (_distanceTo[sourceVertex] != 0.0 || _edgeTo[sourceVertex] != null)
{
return(false);
}
for (int v = 0; v < graph.NumberOfVertices; v++)
{
if (v == sourceVertex)
{
continue;
}
if (_edgeTo[v] == null && _distanceTo[v] != double.PositiveInfinity)
{
return(false);
}
}
for (int v = 0; v < graph.NumberOfVertices; v++)
{
foreach (DirectedEdge edge in graph.Adjacent(v))
{
int w = edge.To;
if (_distanceTo[v] + edge.Weight < _distanceTo[w])
{
return(false);
}
}
}
for (int w = 0; w < graph.NumberOfVertices; w++)
{
if (_edgeTo[w] == null)
{
continue;
}
DirectedEdge edge = _edgeTo[w];
int v = edge.From;
if (w != edge.To)
{
return(false);
}
if (_distanceTo[v] + edge.Weight != _distanceTo[w])
{
return(false);
}
}
return(true);
}
private DijkstraShortestPath(EdgeWeightedDigraph graph, int sourceVertex, int?destinationVertex)
{
if (graph == null)
{
throw new ArgumentNullException("graph", "EdgeWeightedDigraph cannot be null");
}
foreach (DirectedEdge edge in graph.Edges())
{
if (edge.Weight < 0)
{
throw new ArgumentOutOfRangeException(string.Format("Edge: '{0}' has negative weight", edge));
}
}
_distanceTo = new double[graph.NumberOfVertices];
_edgeTo = new DirectedEdge[graph.NumberOfVertices];
for (int v = 0; v < graph.NumberOfVertices; v++)
{
_distanceTo[v] = Double.PositiveInfinity;
}
_distanceTo[sourceVertex] = 0.0;
_priorityQueue = new IndexMinPriorityQueue <double>(graph.NumberOfVertices);
_priorityQueue.Insert(sourceVertex, _distanceTo[sourceVertex]);
while (!_priorityQueue.IsEmpty())
{
int v = _priorityQueue.DeleteMin();
if (destinationVertex.HasValue && v == destinationVertex.Value)
{
return;
}
foreach (DirectedEdge edge in graph.Adjacent(v))
{
Relax(edge);
}
}
}
/// <summary>
/// Returns an IEnumerable of DirectedEdges representing a shortest path from the specified sourceVertex to the specified destinationVertex
/// This is more efficent than creating a new DijkstraShorestPath instance and calling PathTo( destinationVertex ) when we only
/// want a single path from Source to Destination and don't want many paths from the source to multiple different destinations.
/// </summary>
/// <param name="graph">The edge-weighted directed graph</param>
/// <param name="sourceVertex">The source vertext to find a shortest path from</param>
/// <param name="destinationVertex">The destination vertex to find a shortest path to</param>
/// <returns>IEnumerable of DirectedEdges representing a shortest path from the sourceVertex to the specified destinationVertex</returns>
public static IEnumerable <DirectedEdge> FindPath(EdgeWeightedDigraph graph, int sourceVertex, int destinationVertex)
{
var dijkstraShortestPath = new DijkstraShortestPath(graph, sourceVertex, destinationVertex);
return(dijkstraShortestPath.PathTo(destinationVertex));
}
/// <summary>
/// Computes a shortest paths tree from the specified sourceVertex to every other vertex in the edge-weighted directed graph
/// </summary>
/// <param name="graph">The edge-weighted directed graph</param>
/// <param name="sourceVertex">The source vertex to compute the shortest paths tree from</param>
/// <exception cref="ArgumentOutOfRangeException">Throws an ArgumentOutOfRangeException if an edge weight is negative</exception>
/// <exception cref="ArgumentNullException">Thrown if EdgeWeightedDigraph is null</exception>
public DijkstraShortestPath(EdgeWeightedDigraph graph, int sourceVertex)
: this(graph, sourceVertex, null)
{
}
