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’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).

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
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.

Thanks a lot Tyler for pointing out the mistake 🙂

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?

I think you only need to set your node count to M * N.

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.

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.

5. iliyaz

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

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