//
// Find the dual-shortest paths of the PathGraph; implements Suurballe's algorithm
//
public long dualShortestPath(int start, int goal, List <int> actualPath1, List <int> actualPath2)
{
actualPath1.Clear();
actualPath2.Clear();
// Are the given start and goal nodes valid?
if (start <= 0 || goal > graph.NumVertices() || goal <= 0 || start > graph.NumVertices())
{
Debug.WriteLine("Start Node or Goal Node specified is invalid.");
return(-1);
}
// Create a new PathGraph such that every node is duplicated and split into x' and x''
// Incoming nodes go to x', outgoing edges go from x''
// The weight between x' and x'' is zero 0
graph.InduceVertexDisjoint();
updateStartGoalNodes(start, goal);
//
// Find the first shortest path using Dijkstra's algorithm
//
List <int> firstPath = new List <int>();
int firstLength = Dijkstra(firstPath);
// Check if a path existed
if (firstLength == -1)
{
Debug.WriteLine("No first path was found: (" + start + ", " + goal + ")");
return(-1);
}
if (DEBUG)
{
Debug.WriteLine("First Path: with length (" + firstLength + ")");
}
//
// Reverse the used edges
//
reverseShortestPathEdges(firstPath);
//
// Find the second shortest path using Dijkstra's algorithm on the PathGraph with reversed edges
//
List <int> secondPath = new List <int>();
int secondLength = Dijkstra(secondPath);
// Check if a path existed
if (secondLength == -1)
{
Debug.WriteLine("No second path was found: (" + start + ", " + goal + ")");
return(-1);
}
if (DEBUG)
{
Debug.WriteLine("Second Path: with length (" + secondLength + ")");
}
//
// Compare the paths looking for common edges
// Calculate the length of the dual-shortest paths subtracting the common edges
// Split the paths to creates two vertex-disjoint paths
//
List <int> tempPath1 = new List <int>();
List <int> tempPath2 = new List <int>();
int combinedPathLength = combinePaths(firstPath, secondPath, firstLength, secondLength, tempPath1, tempPath2);
//
// Condense the path back down from x'->x'' to x
//
condensePath(tempPath1, actualPath1);
condensePath(tempPath2, actualPath2);
return(combinedPathLength);
}
