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Algorithms: Graph Traversal : Depth First Search ( with C Program source code)



Depth-First Search

Depth-first search algorithm searches deeper in graph whenever possible. In this, edges are explored out of the most recently visited vertex that still has unexplored edges leaving it. When all the vertices of that vertex’s edges have been explored, the search goes backtracks to explore edges leaving the vertex from which a vertex was recently discovered. This process continues until we have discovered all the vertices that are reachable from the original source vertex. It works on both directed and undirected graphs.

Click here, or on the image below to check out Java Applet Visualizations of Depth and Breadth First Search

















Analysis


The DFS function is called exactly once for every vertex that is reachable from the start vertex. Each call looks at the successors of the current vertex, so total time is O(# reachable nodes + total # of outgoing edges from those nodes). The running time of DFS is therefore O(V + E). 

Complete Tutorial with Examples :



Depth First Search - C Program Source code


#include<stdio.h>
#include<assert.h>
/* maxVertices represents maximum number of vertices that can be present in the graph. */
#define maxVertices   100
void Dfs(int graph[][maxVertices], int *size, int presentVertex,int *visited)
{
        printf
("Now visiting vertex %d\n",presentVertex);
        visited
[presentVertex] = 1;
       
/* Iterate through all the vertices connected to the presentVertex and perform dfs on those
           vertices if they are not visited before */

       
int iter;
       
for(iter=0;iter<size[presentVertex];iter++)
       
{
               
if(!visited[graph[presentVertex][iter]])
               
{
                       
Dfs(graph,size,graph[presentVertex][iter],visited);
               
}
       
}
       
return;
       

}
/* Input Format: Graph is directed and unweighted. First two integers must be number of vertces and edges
   which must be followed by pairs of vertices which has an edge between them. */

int main()
{
       
int graph[maxVertices][maxVertices],size[maxVertices]={0},visited[maxVertices]={0};
       
int vertices,edges,iter;
       
/* vertices represent number of vertices and edges represent number of edges in the graph. */
        scanf
("%d%d",&vertices,&edges);
       
int vertex1,vertex2;
       
for(iter=0;iter<edges;iter++)
       
{
                scanf
("%d%d",&vertex1,&vertex2);
                assert
(vertex1>=0 && vertex1<vertices);
                assert
(vertex2>=0 && vertex2<vertices);
                graph
[vertex1][size[vertex1]++] = vertex2;
       
}
       
int presentVertex;
       
for(presentVertex=0;presentVertex<vertices;presentVertex++)
       
{
               
if(!visited[presentVertex])
               
{
                       
Dfs(graph,size,presentVertex,visited);
               
}
       
}
       
return 0;



}

Quick Notes about the Algorithm and the code:


Input Format: Graph is directed and unweighted. First two integers must be number of vertices and edges which must be followed by pairs of vertices which has an edge between them.

maxVertices represents maximum number of vertices that can be present in the graph.
vertices represent number of vertices and edges represent number of edges in the graph.
graph[i][j] represent the weight of edge joining i and j.
size[maxVertices] is initialed to{0}, represents the size of every vertex i.e. the number of edges corresponding to the vertex.
visited[maxVertices]={0} represents the vertex that have been visited.
Initialize the graph.
For presentVertex = 0 to vertices if visited[presentVertex] is 0, i.e. if the vertex has not been visited then call Dfs function. 
presentVertex represents the vertex that is being tackled.
Dfs function is called to get the shortest path.

Dfs function


This function takes the graph obtained (graph[ ][ maxVertices]), pointer to the array size and visited, and the presentValue as arguments.
Print the vertex that is being visited now, which is presentVertex
visited[presentVertex] = 1 as the vertex has now been visited.
Iterate through all the vertices connected to the presentVertex and perform Dfs on those vertices that are not visited before
For iter=0 to size[presentVertex]-1
    if (!visited[graph[presentVertex][iter]])
    Dfs(graph,size,graph[presentVertex][iter],visited)
next


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