Question

Hi I need help with a breadth first and depth first search in C++. If you could please help me with the code for dfs, bfs, and dfsRecursiv functions.

Answer 1

BFS:

For the graph :

0

/ \

1    2

/

3

If we pick source as node 0 , than in bfs , we go breadth-wise i.e first visit all edges from a parent node and the go the child node

1) 0->1

2)0->2

3)1->3

So the bfs sequence is 0 1 2 3

Overall running time using adjacency matrix is O(N^2) , where N is the number of vertices.

Code:

#include <bits/stdc++.h>
using namespace std;

// itialize number of vertices and edges here so we need not to pass them to bfs method seperately.

   const int vertices = 4, edges = 3;
   int adj[vertices][vertices]={{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}};

void BFS(int source)
{

// initially all the nodes are unvisited , so set vis array to 0 for all nodes.
   int vis[vertices+1];
   for(int i=0;i<vertices;i++)
   vis[i]=0;
  
// we would use a vector to act as a queue for storing nodes, you could use STL queue also
// it would also work.
   vector<int> q;
// push the source node in queue.
   q.push_back(source);

// mark it as visited
  
   vis[source] = true;

   int node;
  
// while the queue is not empty
   while (!q.empty()) {
       node = q[0];

// print the node at front of the queue  
       cout << node << " ";
// erase the node at front of the queue
       q.erase(q.begin());

// iterate on the adjacency matrix , if adj[node][i] ==1 means edge from node->i exists
// and it is not visited then , than push it to queue and mark it as visited.
       for (int i = 0; i < vertices; i++) {
           if (adj[node][i] == 1 && (!vis[i])) {
   q.push_back(i);
   vis[i] = true;
           }
       }
   }
}

int main()
{

// adding edge 0-1
   adj[0][1]=1;
// adding edge 0-2
adj[0][2]=1;
// adding edge 1-3
   adj[1][3]=1;
  
// starting bfs from source node->0
   BFS(0);
}

Screenshots:

Output:

DFS:

For the graph :

0

/ \

1    2

/

3

If we pick the vertex 0 as source node , then we will visit the graph in following sequence if we go depthwise fromsource ->

1)0->1

2)1->3

3)0->2

Therefore dfs sequence is 0 1 3 2

Code:

#include <bits/stdc++.h>
using namespace std;

// itialize number of vertices, edges and visted array here so we need
//not to pass them to dfs method seperately.

   const int vertices = 4, edges = 3;
   int adj[vertices][vertices]={{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}};
   int vis[]={0,0,0,0};

void DFS(int node)
{
  
// Print the current node
cout <<node << " ";
  
// mark node as visited after printing i.e assign 1 to vis[node].
vis[node] = 1;
  
// Iterate on the adjacency matrix and if the edge from node->i exists and is not visited
// start a recursive call to dfs method with new node i .
for (int i = 0; i < vertices; i++) {
  
// If some node is adjacent to the current node
// and it has not already been visited
if (adj[node][i] == 1 && (!vis[i])) {
DFS(i);
}
}
}

int main()
{

// adding edge 0-1
   adj[0][1]=1;
// adding edge 0-2
adj[0][2]=1;
// adding edge 1-3
   adj[1][3]=1;
  
// starting dfs from source node->0

   DFS(0);
}

Output:

Note : dfs and dfsRecursive method will be same because i have already implement dfs recursively.

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