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.

52 thoughts on “Dijkstra’s Algorithm in C”

  1. 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.

      1. 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.

  2. 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?

  3. 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.

  4. 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.

  5. prathik vijaykumar

    hey the code is running properly for 9 vertices, but is giving problems when the number of vertices are 16. your help will be valuable

    1. Your matrix is ti big, change the variable MAX to be 25 or 26, to be safe. You can find it in the first line of codes wheere is the keyword DEFINE

  6. hi, im having problem for my assignment. i have assign to do a shortest path in GPS system code in c.
    where i need to create a map or path and ask the user to insert starting point and destination and we also have to calculate and display 3 shortest path based on ranking and display the history record

  7. Dear Author
    Please help me to created shorthest path and longest path distance in one program , how to add longest path distance in that code in dev c++ ? . i have try but always error for add longest path distance Please help me , i beg to you for my assignment , please sir help me . you can send in my email the code , anyone please help me , its important.
    Email : [email protected]

  8. hello,
    nice code , but i think something is missing.
    your program will show the paths to the other nodes but , if I want the shortest path from a specific source to a specific destination?
    one more variable is required

  9. Programs are witten in difficult ways.
    What I found that a program is considered best in written complex way.

    But any software program is considered in written is simple and understandable manner.
    There might be hundreds of ways to write A+B=C but in India the one with max number of code lines would fetch max marks irrespective if its worth or fuddu

  10. Sankalp Arora

    Why haven’t we first created a graph and then used its adjacency matrix, for further work. Isn’t it wrong just to have a 2-D array and applying the stuff to it?

  11. 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.

  12. Hello,
    Can you please explain me how it works?
    for(i=0;i<n;i++)
    if(i!=startnode)
    {
    printf("\nDistance of node%d=%d",i,distance[i]);
    printf("\nPath=%d",i);

    j=i;
    do
    {
    j=pred[j];
    printf("<-%d",j);
    }while(j!=startnode);
    }
    why pred[j] is the previus node?

  13. Hi , thank you for this beautiful code, now i understand Djikstra algorithm 🙂
    I’ll use it to model points and streets on a map to find the shortest driving way, like GPS 😀

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