public List <int> GetShortestPath(CustomGraph graph, int sourceIndex, int destinationIndex)
{
FinalDistance = new Dictionary <int, int>();
ParentBacktrack = new Dictionary <int, int>();
foreach (int vertexIndex in graph.AllVertexIndices.Keys)
{
FinalDistance[vertexIndex] = int.MaxValue;
}
FinalDistance[sourceIndex] = 0;
ParentBacktrack[sourceIndex] = -1; // we can use this value are termination condition while backtracking to find the path
for (int i = 0; i < graph.AllVertexIndices.Count - 1; i++) // We need to do V-1 iterations
{
foreach (GraphEdge edge in graph.AllEdges)
{
int currentDistance = (FinalDistance[edge.StartVertexId] != int.MaxValue) ? FinalDistance[edge.StartVertexId] + edge.Weight : int.MaxValue;
if (FinalDistance[edge.EndVertexId] > currentDistance)
{
FinalDistance[edge.EndVertexId] = currentDistance;
ParentBacktrack[edge.EndVertexId] = edge.StartVertexId;
}
}
}
// Detect Negative cycle: we can detect the negative cycle in the graph by doing the above operations one more time and make sure we dont get
// a lesser value for the final distance for any other vertex
foreach (GraphEdge edge in graph.AllEdges)
{
int currentDistance = (FinalDistance[edge.StartVertexId] != int.MaxValue) ? FinalDistance[edge.StartVertexId] + edge.Weight : int.MaxValue;
if (FinalDistance[edge.EndVertexId] > currentDistance)
{
throw new Exception("Negative cycle detected");
}
}
if (FinalDistance[destinationIndex] != int.MaxValue)
{
return(BackTrackToGetPath(destinationIndex));
}
else
{
// we dont have a path from source to destination
return(null);
}
}
public static void TestBellmanFord()
{
CustomGraph graph = new CustomGraph();
graph.AddEdge(3, 4, 2);
graph.AddEdge(4, 3, 1);
graph.AddEdge(2, 4, 4);
graph.AddEdge(0, 2, 5);
graph.AddEdge(1, 2, -3);
graph.AddEdge(0, 3, 8);
graph.AddEdge(0, 1, 4);
BellmanFord bf = new BellmanFord();
List <int> shortestPath = bf.GetShortestPath(graph, 0, 2);
Console.WriteLine("The shortest distance from {0} to {1} is {2}", 0, 2, bf.FinalDistance[2]);
PrintPath(shortestPath);
shortestPath = bf.GetShortestPath(graph, 0, 4);
Console.WriteLine("The shortest distance from {0} to {1} is {2}", 0, 4, bf.FinalDistance[4]);
PrintPath(shortestPath);
shortestPath = bf.GetShortestPath(graph, 0, 3);
Console.WriteLine("The shortest distance from {0} to {1} is {2}", 0, 3, bf.FinalDistance[3]);
PrintPath(shortestPath);
Console.WriteLine("Adding negative cycle to the graph");
graph.AddEdge(2, 0, -2);
try
{
shortestPath = bf.GetShortestPath(graph, 0, 2);
}
catch (Exception exp)
{
Console.WriteLine(exp.Message);
}
}
