Program Explanation

This program implements Dijkstra’s Algorithm to find the shortest path from a source vertex to all other vertices in a weighted graph.
The graph is represented using an adjacency matrix, and the algorithm efficiently computes the shortest distances.

Program Structure

• Constants and Includes: Standard libraries are included for input/output and maximum values.
• Function Prototypes: Functions for the main algorithm and for printing results are declared.
• Main Function: Initializes the graph, sets the source vertex, and calls the Dijkstra function.
• Dijkstra Function: Implements the algorithm to calculate the shortest paths.
• Print Function: Displays the shortest path from the source to each vertex.

Code

#include 
#include 
#include 

#define V 5 // Number of vertices in the graph

// Function prototypes
int minDistance(int dist[], bool sptSet[]);
void dijkstra(int graph[V][V], int src);
void printSolution(int dist[], int n);

int main() {
    // Example graph represented as an adjacency matrix
    int graph[V][V] = {
        {0, 10, 0, 30, 100},
        {10, 0, 50, 0, 0},
        {0, 50, 0, 20, 10},
        {30, 0, 20, 0, 60},
        {100, 0, 10, 60, 0}
    };

    dijkstra(graph, 0); // Call Dijkstra's algorithm from source vertex 0
    return 0;
}

// Function to find the vertex with the minimum distance value
int minDistance(int dist[], bool sptSet[]) {
    int min = INT_MAX, min_index;

    for (int v = 0; v < V; v++) {
        if (sptSet[v] == false && dist[v] <= min) {
            min = dist[v];
            min_index = v;
        }
    }
    return min_index;
}

// Function that implements Dijkstra's algorithm
void dijkstra(int graph[V][V], int src) {
    int dist[V]; // Output array dist[i] holds the shortest distance from src to j
    bool sptSet[V]; // sptSet[i] will be true if vertex i is included in shortest path tree

    // Initialize all distances as infinite and sptSet[] as false
    for (int i = 0; i < V; i++) {
        dist[i] = INT_MAX;
        sptSet[i] = false;
    }

    // Distance from source to 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
        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] if and only if it's not in sptSet, there is an edge from u to v,
            // and the total weight of path from src to v through u is smaller than current value of dist[v]
            if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX && dist[u] + graph[u][v] < dist[v]) {
                dist[v] = dist[u] + graph[u][v];
            }
        }
    }

    // Print the constructed distance array
    printSolution(dist, V);
}

// Function to print the constructed distance array
void printSolution(int dist[], int n) {
    printf("Vertex Distance from Source\n");
    for (int i = 0; i < n; i++) {
        printf("%d \t\t %d\n", i, dist[i]);
    }
}

How to Compile and Run

1. Copy the code into a file named dijkstra.c.
2. Open a terminal and navigate to the directory containing the file.
3. Compile the code using gcc dijkstra.c -o dijkstra.
4. Run the program with ./dijkstra.

Conclusion

Dijkstra’s Algorithm is a powerful tool for finding the shortest paths in a graph.
This C implementation provides a clear understanding of how the algorithm works, and can be extended for larger graphs or modified for different use cases.