Another single source shortest path algorithm is Dijkstra’s shortest path algorithm. We learned Bellman-Ford’s algorithm which runs on O (V.E) but well implemented Dijkstra’s algorithm can run on lower running time than Bellman-Ford’s algorithm, only limitation is all the edges should have positive weights.

Implementation

    We have to use priority queue which have learned in previous article, we reuse same code by adding reference of priority queue project in current project. Now we will create class for Vertex.

public class Vertex
{
    public string Name { get; set; }
    public int D { get; set; }
    public Vertex Parent { get; set; }
}

We will reuse same methods "InitializeSingleSource" and "Relax" from Bellman-Ford’s algorithm.  

public static void InitializeSingleSource(Vertex[] vertices, Vertex s)
{
    foreach (Vertex v in vertices)
    {
        v.D = int.MaxValue;
        v.Parent = null;
    }
    s.D = 0;
}

public static void Relax(Vertex u, Vertex v, int weight)
{
    if (v.D > u.D + weight)
    {
        v.D = u.D + weight;
        v.Parent = u;
    }
}

Now Let’s implement Dijkstra’s algorithm:

public static List<Vertex> Dijkstra(Vertex[] vertices, int[][] graph, int source)
{
    InitializeSingleSource(vertices, vertices[source]);
    List<Vertex> result = new List<Vertex>();
    //adding all vertex to priority queue
    PriorityQueue.PriorityQueue<Vertex> queue = new PriorityQueue.PriorityQueue<Vertex>(true);
    for (int i = 0; i < vertices.Length; i++)
        queue.Enqueue(vertices[i].D, vertices[i]);

    //treversing to all vertices
    while (queue.Count > 0)
    {
        var u = queue.Dequeue();
        result.Add(u);
        //again traversing to all vertices
        for (int v = 0; v < graph[Convert.ToInt32(u.Name)].Length; v++)
        {
            if (graph[Convert.ToInt32(u.Name)][v] > 0)
            {
                Relax(u, vertices[v], graph[Convert.ToInt32(u.Name)][v]);
                //updating priority value since distance is changed
                queue.UpdatePriority(vertices[v], vertices[v].D);
            }
        }
    }
    return result;
}

Let’s implement method to print the shortest path

public static void PrintPath(Vertex u, Vertex v, List<Vertex> vertices)
{
    if (v != u)
    {
        PrintPath(u, v.Parent, vertices);
        Console.WriteLine("Vertax {0} weight: {1}", v.Name, v.D);
    }
    else
        Console.WriteLine("Vertax {0} weight: {1}", v.Name, v.D);
}

Running above code:

static void Main(string[] args)
{
    int[][] adjacencyMatrix = new int[][] { new int[] { 0,0,0,3,12 },
                                    new int[] { 0,0,2,0,0 },
                                    new int[] { 0,0,0,-2,0 },
                                    new int[] { 0,5,3,0,0 },
                                    new int[] { 0,0,7,0,0 } };
    Vertex[] vertices = new Vertex[adjacencyMatrix.GetLength(0)];
    //Source vertex
    int source = 0;

    for (int i = 0; i < vertices.Length; i++)
        vertices[i] = new Vertex() { Name = i.ToString() };
    //calling dijkstra  algorithm
    List<Vertex> result = Dijkstra(vertices, adjacencyMatrix, source);
    //printing distance
    PrintPath(vertices[0], vertices[2], result);
    Console.ReadLine();
}

Output:

Vertax 0 weight: 0

Vertax 3 weight: 3

Vertax 2 weight: 6