Dijkstra’s Algorithm in C

Here you will learn about dijkstra’s algorithm in C.
 
Dijkstra algorithm is also called single source shortest path algorithm. It is based on greedy technique. The algorithm maintains a list visited[ ] of vertices, whose shortest distance from the source is already known.
 
If visited[1], equals 1, then the shortest distance of vertex i is already known. Initially, visited[i] is marked as, for source vertex.
 
At each step, we mark visited[v] as 1. Vertex v is a vertex at shortest distance from the source vertex. At each step of the algorithm, shortest distance of each vertex is stored in an array distance[ ].
Dijkstra Animation 
 

Dijkstra’s Algorithm

1. Create cost matrix C[ ][ ] from adjacency matrix adj[ ][ ]. C[i][j] is the cost of going from vertex i to vertex j. If there is no edge between vertices i and j then C[i][j] is infinity.
 
2. Array visited[ ] is initialized to zero.
               for(i=0;i<n;i++)
                              visited[i]=0;
 
3. If the vertex 0 is the source vertex then visited[0] is marked as 1.
 
4. Create the distance matrix, by storing the cost of vertices from vertex no. 0 to n-1 from the source vertex 0.
               for(i=1;i<n;i++)
                              distance[i]=cost[0][i];
Initially, distance of source vertex is taken as 0. i.e. distance[0]=0;
 
5. for(i=1;i<n;i++)
– Choose a vertex w, such that distance[w] is minimum and visited[w] is 0. Mark visited[w] as 1.
– Recalculate the shortest distance of remaining vertices from the source.
– Only, the vertices not marked as 1 in array visited[ ] should be considered for recalculation of distance. i.e. for each vertex v
               if(visited[v]==0)
                              distance[v]=min(distance[v],
                              distance[w]+cost[w][v])

Time Complexity

The program contains two nested loops each of which has a complexity of O(n). n is number of vertices. So the complexity of algorithm is O(n2).
 
Dijkstra Algorithm for Finding Shortest Path of a Graph
 

Program for Dijkstra’s Algorithm in C

C Program on Dijkstra Algorithm for Finding Minimum Distance of Vertices from a Given Source in a Graph

Output
C Program on Dijkstra Algorithm for Finding Minimum Distance of Vertices from a Given Source in a Graph
Comment below if you found something wrong in above dijkstra’s algorithm in C.

15 thoughts on “Dijkstra’s Algorithm in C

  1. Tyler

    You have a typo in step 2. The for loop should be (for i = 0; i < n; i++) visited[i] = 0; You have a "1" in the brackets so the for loop is pointless by initializing the second element over and over, n times.

    Reply
  2. polarBear

    What would need to be changed in the algorithm if we have a rectangular matrix n*m? Because I have a maze of size n*m and I need to find shortest path from some spot in the maze to the exit. Any help with that?

    Reply
  3. Kostas

    im trying to short out how to make it show the distance and the path between 2 points and not all, for instance if i want to go from a to b what is the best path and the cost.

    Reply
  4. Shrinivas

    Can you please help me to convert this code to find longest path, I have tried but few problems are coming. Its very important to me, your help is more precious.

    Reply
  5. iliyaz

    thanks dear, it is very nice program for understanding…………..

    Reply
  6. supriya

    nice website. here everything is given detailed. convenient way to study for student.

    Reply
  7. farah

    this website is amazing.codes are easily understandable.i always follow this website.

    Reply
  8. mkhoda

    Hey, could you please modify your code to find the k-shortest path. It would be much appreciated. Thanks

    Reply

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