#include <stdio.h >
#include <stdbool.h>
#define V 5
void DFSUtil(int graph[V][V], int v, bool visited[]) {
    visited[v] = true;
    printf("%d ", v);
    for (int i = 0; i < V; i++) {
        if (graph[v][i] == 1 && !visited[i]) {
            DFSUtil(graph, i, visited);
        }
    }
}

void DFS(int graph[V][V]) {
    bool visited[V] = {false};
    for (int i = 0; i < V; i++) {
        if (!visited[i]) {
            DFSUtil(graph, i, visited);
        }
    }
}

int main() {
    int graph[V][V] = {
        {0, 1, 1, 0, 0},
        {1, 0, 0, 1, 1},
        {1, 0, 0, 0, 0},
        {0, 1, 0, 0, 1},
        {0, 1, 0, 1, 0}
    };

    printf("Depth First Traversal:\n");
    DFS(graph);
    return 0;
}

#include <stdio.h>
#include <limits.h>
#include <stdbool.h> // Include stdbool.h for using bool type
#define V 9 // Number of vertices in the graph

// 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] && dist[v] <= min) {
            min = dist[v];
            min_index = v;
        }
    }
    return min_index;
}

// Function to implement Dijkstra's single source shortest path algorithm

void dijkstra(int graph[V][V], int src) {
    int dist[V];   // Output array to hold the shortest distances
    bool sptSet[V]; // True if vertex is included in the shortest path tree

    // Initialize distances to all vertices as infinite and sptSet[] as false

    for (int i = 0; i < V; i++) {
        dist[i] = INT_MAX;
        sptSet[i] = false;
    }

    // Distance to the source vertex is always 0
    dist[src] = 0;

    // Find the 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 chosen vertex as processed
        sptSet[u] = true;

        // Update dist[] for the adjacent vertices of the chosen vertex
        for (int v = 0; v < V; v++) {
            // Update dist[v] if:
            // 1. Vertex v is not in the shortest path tree
            // 2. There is an edge from u to v
            // 3. The total weight of the path from src to v through u is smaller than the 
            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 result

    printf("Vertex   Distance from Source\n");
    for (int i = 0; i < V; i++) {
        printf("%d tt %d\n", i, dist[i]);
    }
}

int main() {
    // Graph represented as an adjacency matrix

    int graph[V][V] = { { 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 } };

    // Run Dijkstra's algorithm
    dijkstra(graph, 0);

    return 0;
}