Shortest Path In Graph – Dijkstra’s Algorithm – C# Implementation

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In this article, we will learn C# implementation of Dijkstra Algorithm for Determining the Shortest Path

Dijkstra’s algorithm is an algorithm for finding the shortest paths between nodes in a graph.It was conceived by computer scientist Edsger W. Dijkstra in 1956.This algorithm helps to find the shortest path from a point in a graph (the source) to a destination.

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

using System.Diagnostics;

namespace DijkstraAlgorithm

{

    class Dijkstra

    {

        private static int MinimumDistance(int[] distance, bool[] shortestPathTreeSet, int verticesCount)

        {

            int min = int.MaxValue;

            int minIndex = 0;

            for (int v = 0; v < verticesCount; ++v)

            {

                if (shortestPathTreeSet[v] == false && distance[v] <= min)

                {

                    min = distance[v];

                    minIndex = v;

                }

            }

            return minIndex;

        }

        private static void Print(int[] distance, int verticesCount)

        {

            Console.WriteLine("Vertex    Distance from source");

            for (int i = 0; i < verticesCount; ++i)

                Console.WriteLine("{0}\t  {1}", i, distance[i]);

        }

        public static void DijkstraAlgo(int[,] graph, int source, int verticesCount)

        {

            int[] distance = new int[verticesCount];

            bool[] shortestPathTreeSet = new bool[verticesCount];

            for (int i = 0; i < verticesCount; ++i)

            {

                distance[i] = int.MaxValue;

                shortestPathTreeSet[i] = false;

            }

            distance[source] = 0;

            for (int count = 0; count < verticesCount - 1; ++count)

            {

                int u = MinimumDistance(distance, shortestPathTreeSet, verticesCount);

                shortestPathTreeSet[u] = true;

                for (int v = 0; v < verticesCount; ++v)

                    if (!shortestPathTreeSet[v] && Convert.ToBoolean(graph[u, v]) && distance[u] != int.MaxValue && distance[u] + graph[u, v] < distance[v])

                        distance[v] = distance[u] + graph[u, v];

            }

            Print(distance, verticesCount);

        }

        static void Main(string[] args)

        {

            int[,] graph =  {

                         { 0, 6, 0, 0, 0, 0, 0, 9, 0 },

                         { 6, 0, 9, 0, 0, 0, 0, 11, 0 },

                         { 0, 9, 0, 5, 0, 6, 0, 0, 2 },

                         { 0, 0, 5, 0, 9, 16, 0, 0, 0 },

                         { 0, 0, 0, 9, 0, 10, 0, 0, 0 },

                         { 0, 0, 6, 0, 10, 0, 2, 0, 0 },

                         { 0, 0, 0, 16, 0, 2, 0, 1, 6 },

                         { 9, 11, 0, 0, 0, 0, 1, 0, 5 },

                         { 0, 0, 2, 0, 0, 0, 6, 5, 0 }

                            };

            DijkstraAlgo(graph, 0, 9);

        }

    }

}

Output:

Vertex Distance from source
0  0
1  6
2  15
3  20
4  22
5  12
6  10
7  9
8  14
Press any key to continue…

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C# Program for Dijkstra’s shortest path algorithm | Greedy Algo-7

Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph.

Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree. Like Prim’s MST, we generate a SPT (shortest path tree) with given source as root. We maintain two sets, one set contains vertices included in shortest path tree, other set includes vertices not yet included in shortest path tree. At every step of the algorithm, we find a vertex which is in the other set (set of not yet included) and has a minimum distance from the source.

Below are the detailed steps used in Dijkstra’s algorithm to find the shortest path from a single source vertex to all other vertices in the given graph.
Algorithm
1) Create a set sptSet (shortest path tree set) that keeps track of vertices included in shortest path tree, i.e., whose minimum distance from source is calculated and finalized. Initially, this set is empty.
2) Assign a distance value to all vertices in the input graph. Initialize all distance values as INFINITE. Assign distance value as 0 for the source vertex so that it is picked first.
3) While sptSet doesn’t include all vertices
….a) Pick a vertex u which is not there in sptSet and has minimum distance value.
….b) Include u to sptSet.
….c) Update distance value of all adjacent vertices of u. To update the distance values, iterate through all adjacent vertices. For every adjacent vertex v, if sum of distance value of u (from source) and weight of edge u-v, is less than the distance value of v, then update the distance value of v.

// A C# program for Dijkstra's single

// source shortest path algorithm.

// The program is for adjacency matrix

// representation of the graph

using System;

class GFG {

    // A utility function to find the

    // vertex with minimum distance

    // value, from the set of vertices

    // not yet included in shortest

    // path tree

    static int V = 9;

    int minDistance(int[] dist,

                    bool[] sptSet)

    {

        // Initialize min value

        int min = int.MaxValue, min_index = -1;

        for (int v = 0; v < V; v++)

            if (sptSet[v] == false && dist[v] <= min) {

                min = dist[v];

                min_index = v;

            }

        return min_index;

    }

    // A utility function to print

    // the constructed distance array

    void printSolution(int[] dist, int n)

    {

        Console.Write("Vertex     Distance "

                      + "from Source\n");

        for (int i = 0; i < V; i++)

            Console.Write(i + " \t\t " + dist[i] + "\n");

    }

    // Funtion that implements Dijkstra's

    // single source shortest path algorithm

    // for a graph represented using adjacency

    // matrix representation

    void dijkstra(int[, ] graph, int src)

    {

        int[] dist = new int[V]; // The output array. dist[i]

        // will hold the shortest

        // distance from src to i

        // sptSet[i] will true if vertex

        // i is included in shortest path

        // tree or shortest distance from

        // src to i is finalized

        bool[] sptSet = new bool[V];

        // Initialize all distances as

        // INFINITE and stpSet[] as false

        for (int i = 0; i < V; i++) {

            dist[i] = int.MaxValue;

            sptSet[i] = false;

        }

        // Distance of source vertex

        // from itself is always 0

        dist[src] = 0;

        // Find shortest path for all vertices

        for (int count = 0; count < V - 1; count++) {

            // Pick the minimum distance vertex

            // from the set of vertices not yet

            // processed. u is always equal to

            // src in first iteration.

            int u = minDistance(dist, sptSet);

            // Mark the picked vertex as processed

            sptSet[u] = true;

            // Update dist value of the adjacent

            // vertices of the picked vertex.

            for (int v = 0; v < V; v++)

                // Update dist[v] only if is not in

                // sptSet, there is an edge from u

                // to v, and total weight of path

                // from src to v through u is smaller

                // than current value of dist[v]

                if (!sptSet[v] && graph[u, v] != 0 && 

                     dist[u] != int.MaxValue && dist[u] + graph[u, v] < dist[v])

                    dist[v] = dist[u] + graph[u, v];

        }

        // print the constructed distance array

        printSolution(dist, V);

    }

    // Driver Code

    public static void Main()

    {

        /* Let us create the example 

graph discussed above */

        int[, ] graph = new int[, ] { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },

                                      { 4, 0, 8, 0, 0, 0, 0, 11, 0 },

                                      { 0, 8, 0, 7, 0, 4, 0, 0, 2 },

                                      { 0, 0, 7, 0, 9, 14, 0, 0, 0 },

                                      { 0, 0, 0, 9, 0, 10, 0, 0, 0 },

                                      { 0, 0, 4, 14, 10, 0, 2, 0, 0 },

                                      { 0, 0, 0, 0, 0, 2, 0, 1, 6 },

                                      { 8, 11, 0, 0, 0, 0, 1, 0, 7 },

                                      { 0, 0, 2, 0, 0, 0, 6, 7, 0 } };

        GFG t = new GFG();

        t.dijkstra(graph, 0);

    }

}

// This code is contributed by ChitraNayal

Output:

Vertex     Distance from Source

0          0

1          4

2          12

3          19

4          21

5          11

6          9

7          8

8          14

Please refer complete article on Dijkstra’s shortest path algorithm | Greedy Algo-7 for more details!

Links:

1.      https://www.videlin.eu/2016/04/28/shortest-path-in-graph-dijkstras-algorithm-c-implementation/

2.      https://www.csharpstar.com/dijkstra-algorithm-csharp/

3.      https://www.geeksforgeeks.org/csharp-program-for-dijkstras-shortest-path-algorithm-greedy-algo-7/

4.      https://en.wikipedia.org/wiki/Adjacency_matrix

5.      https://www.thecrazyprogrammer.com/2014/03/representation-of-graphs-adjacency-matrix-and-adjacency-list.html

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