Depth First Search (DFS) Traversal of a Graph [Algorithm and Program]

Depth First Search (DFS)

It is like preorder traversal of tree
. Traversal can start from any vertex, say V. Vis visited and then all vertices adjacent to Vi are traversed recursively using DFS.
Since, a graph can have cycles. We must avoid revisiting a node. To do this, when we visit a vertex V, we mark it visited. A node that has already been marked as visited should not be selected for traversal. Marking of visited vertices can be done with the help of a global array visited[ ]. Array visited[ ] is initialized to false (0).

Algorithm for DFS

n ← number of nodes
Initialize visited[ ] to false (0)
for(i=0;i<n;i++)
               visited[i] = 0;
void DFS(vertex i) [DFS starting from i]
{
               visited[i]=1;
               for each w adjacent to i
                              if(!visited[w])
                                             DFS(w);
}
Depth First Search (DFS) Traversal of a Graph
he graph shown above is taken as input in both the programs mentioned below:

C Program to implement DFS traversal on a graph represented using an adjacency matrix

#include<stdio.h>
void DFS(int);
int G[10][10],visited[10],n;    //n is no of vertices and graph is sorted in array G[10][10]
void main()
{
    int i,j;
    printf(“Enter number of vertices:”);
    scanf(“%d”,&n);
    //read the adjecency matrix
    printf(“\nEnter adjecency matrix of the graph:”);
    for(i=0;i<n;i++)
        for(j=0;j<n;j++)
            scanf(“%d”,&G[i][j]);
    //visited is initialized to zero
    for(i=0;i<n;i++)
        visited[i]=0;
    DFS(0);
}
void DFS(int i)
{
    int j;
    printf(“\n%d”,i);
    visited[i]=1;
    for(j=0;j<n;j++)
        if(!visited[j]&&G[i][j]==1)
            DFS(j);
}
C Program to implement DFS traversal on a graph represented using an adjacency matrix

C Program to implement DFS traversal on a graph represented using an adjacency list

#include<stdio.h>
typedef struct node
{
    struct node *next;
    int vertex;
}node;
node *G[20];    //heads of linked list
int visited[20];
int n;
void read_graph();  //create adjacency list
void insert(int,int);   //insert an edge (vi,vj) in te adjacency list
void DFS(int);
void main()
{
    int i;
    read_graph();
    //initialised visited to 0
    for(i=0;i<n;i++)
        visited[i]=0;
    DFS(0);
}
void DFS(int i)
{
    node *p;
    printf(“\n%d”,i);
    p=G[i];
    visited[i]=1;
    while(p!=NULL)
    {
        i=p->vertex;
        if(!visited[i])
            DFS(i);
        p=p->next;
    }
}
void read_graph()
{
    int i,vi,vj,no_of_edges;
    printf(“Enter number of vertices:”);
    scanf(“%d”,&n);
    //initialise G[] with a null
    for(i=0;i<n;i++)
    {
        G[i]=NULL;
        //read edges and insert them in G[]
        printf(“Enter number of edges:”);
        scanf(“%d”,&no_of_edges);
        for(i=0;i<no_of_edges;i++)
        {
            printf(“Enter an edge(u,v):”);
            scanf(“%d%d”,&vi,&vj);
            insert(vi,vj);
        }
    }
}
void insert(int vi,int vj)
{
    node *p,*q;
    //acquire memory for the new node
    q=(node*)malloc(sizeof(node));
    q->vertex=vj;
    q->next=NULL;
    //insert the node in the linked list number vi
    if(G[vi]==NULL)
        G[vi]=q;
    else
    {
        //go to end of the linked list
        p=G[vi];
        while(p->next!=NULL)
            p=p->next;
        p->next=q;
    }
}
C Program to implement DFS traversal on a graph represented using an adjacency list
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