How to modify dijkstra algorithm to find all possible paths?

Question

I know that could be asked before already but I cannot find it. I need to modify below dijkstra algorithm which works good for finding shortest path between 2 nodes but I need to find all possible paths also. I know it should be relatively easy to do this but so far I don't have idea how to do this simplest way. I'm using directed weighted graph.

    class Dijkstra
    {
        private List<Node> _nodes;
        private List<Edge> _edges;
        private List<Node> _basis;
        private Dictionary<string, double> _dist;
        private Dictionary<string, Node> _previous;

        public Dijkstra(List<Edge> edges, List<Node> nodes)
        {

            Edges = edges;
            Nodes = nodes;
            Basis = new List<Node>();
            Dist = new Dictionary<string, double>();
            Previous = new Dictionary<string, Node>();

            // record node 
            foreach (Node n in Nodes)
            {
                Previous.Add(n.Name, null);
                Basis.Add(n);
                Dist.Add(n.Name, double.MaxValue);
            }
        }

        /// Calculates the shortest path from the start
        ///  to all other nodes
        public void calculateDistance(Node start)
        {
            Dist[start.Name] = 0;

            while (Basis.Count > 0)
            {
                Node u = getNodeWithSmallestDistance();
                if (u == null)
                {
                    Basis.Clear();
                }
                else
                {
                    foreach (Node v in getNeighbors(u))
                    {
                        double alt = Dist[u.Name] + getDistanceBetween(u, v);
                        if (alt < Dist[v.Name])
                        {
                            Dist[v.Name] = alt;
                            Previous[v.Name] = u;
                        }
                    }
                    Basis.Remove(u);
                }
            }
        }

        public List<Node> getPathTo(Node d)
        {
            List<Node> path = new List<Node>();

            path.Insert(0, d);

            while (Previous[d.Name] != null)
            {
                d = Previous[d.Name];
                path.Insert(0, d);
            }

            return path;
        }

    public Node getNodeWithSmallestDistance()
        {
            double distance = double.MaxValue;
            Node smallest = null;

            foreach (Node n in Basis)
            {
                if (Dist[n.Name] < distance)       
                {
                    distance = Dist[n.Name];
                    smallest = n;
                }
            }

            return smallest;
        }


        public List<Node> getNeighbors(Node n)
        {
            List<Node> neighbors = new List<Node>();

            foreach (Edge e in Edges)
            {
                if (e.Origin.Equals(n) && Basis.Contains(n))
                {
                    neighbors.Add(e.Destination);
                }
            }

            return neighbors;
        }

       public double getDistanceBetween(Node o, Node d)
        {
            foreach (Edge e in Edges)
            {
                if (e.Origin.Equals(o) && e.Destination.Equals(d))
                {
                    return e.Distance;
                }
            }

            return 0;
        }


        public List<Node> Nodes
        {
            get { return _nodes; }
            set { _nodes = value; }
        }

        public List<Edge> Edges
        {
            get { return _edges; }
            set { _edges = value; }
        }

        public List<Node> Basis
        {
            get { return _basis; }
            set { _basis = value; }
        }

        public Dictionary<string, double> Dist
        {
            get { return _dist; }
            set { _dist = value; }
        }

        public Dictionary<string, Node> Previous
        {
            get { return _previous; }
            set { _previous = value; }
        }
    }
}

static void Main(string[] args)
        {
//Nodes initialisation goes here

Dijkstra d = new Dijkstra(_edges, _nodes);
d.calculateDistance(_dictNodes["A"]);
 List<Node> path = d.getPathTo(_dictNodes["C"]);
}

Answer 1

OK, I have actually modified Dijkstra class to do BFS as well and it got me all possible routes. I added this method:

public void BreadthFirst(Edge graph, LinkedList<String> visited) 
{
    LinkedList<String> nodes = graph.adjacentNodes(visited.Last());

    // Examine adjacent nodes
    foreach (String node in nodes) 
    {
        if (visited.Contains(node))
        {
            continue;
        }

        if (node.Equals(endNode))
        {
            visited.AddLast(node);

            printPath(visited);

            visited.RemoveLast();

            break;
         }
     }

    // In breadth-first, recursion needs to come after visiting adjacent nodes
    foreach (String node in nodes)
    {      
        if(visited.Contains(node) || node.Equals(endNode))
        {
            continue;
        }

        visited.AddLast(node);

        // Recursion
        BreadthFirst(graph, visited);

        visited.RemoveLast();
    }
}

Usage would be like this:

Dijkstra d = new Dijkstra(_edges, _nodes);

LinkedList<String> visited = new LinkedList<string>();  //collecting all routes
visited.AddFirst(start);

d.BreadthFirst(graph, visited);

Answer 2

You can not easily modify Dijkstra to show you all the possible paths. You need to modify the BFS or DFS search.

If you try to modify Dijkstra, in the end, you will end with a BFS or DFS search algorithm, so best start from there instead.