Breadth First Search(BFS) and Depth First Search(DFS) Traversal

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;

 class Node
{
        public char label;
        public boolean visited=false;
        public Node(char l)
        {
            this.label=l;
        }
}


class Graph
{
       public Node rootNode;
       public ArrayList nodes=new ArrayList();
       public int[][] adjMatrix;//Edges will be represented as adjacency Matrix
       int size;
       public void setRootNode(Node n)
       {
           this.rootNode=n;
       }
      
       public Node getRootNode()
       {
           return this.rootNode;
       }
      
       public void addNode(Node n)
       {
           nodes.add(n);
       }
      
       //This method will be called to make connect two nodes
       public void connectNode(Node start,Node end)
       {
           if(adjMatrix==null)
           {
               size=nodes.size();
               adjMatrix=new int[size][size];
           }
  
           int startIndex=nodes.indexOf(start);
           int endIndex=nodes.indexOf(end);
           adjMatrix[startIndex][endIndex]=1;
           adjMatrix[endIndex][startIndex]=1;
       }
      
       private Node getUnvisitedChildNode(Node n)
       {
          
           int index=nodes.indexOf(n);
           int j=0;
           while(j<size)
           {
               if(adjMatrix[index][j]==1 && ((Node)nodes.get(j)).visited==false)
               {
                   return (Node)nodes.get(j);
               }
               j++;
           }
           return null;
       }
      
       //BFS traversal of a tree is performed by the bfs() function
       public void bfs()
       {
          
           //BFS uses Queue data structure
           Queue q=new LinkedList();
           q.add(this.rootNode);
           printNode(this.rootNode);
           rootNode.visited=true;
           while(!q.isEmpty())
           {
               Node n=(Node)q.remove();
               Node child=null;
               while((child=getUnvisitedChildNode(n))!=null)
               {
                   child.visited=true;
                   printNode(child);
                   q.add(child);
               }
           }
           //Clear visited property of nodes
           clearNodes();
       }
      
       //DFS traversal of a tree is performed by the dfs() function
       public void dfs()
       {
           //DFS uses Stack data structure
           Stack s=new Stack();
           s.push(this.rootNode);
           rootNode.visited=true;
           printNode(rootNode);
           while(!s.isEmpty())
           {
              Node n=(Node)s.peek();
               Node child=getUnvisitedChildNode(n);
               if(child!=null)
               {
                  child.visited=true;
                  printNode(child);
                  s.push(child);
              }
              else
              {
                 s.pop();
              }
          }
         //Clear visited property of nodes
          clearNodes();
      }
     
     
      //Utility methods for clearing visited property of node
      private void clearNodes()
      {
          int i=0;
         while(i<size)
          {
             Node n=(Node)nodes.get(i);
              n.visited=false;
              i++;
          }
      }
     
      //Utility methods for printing the node's label
     private void printNode(Node n)
      {
          System.out.print(n.label+" ");
      }
 
    
     
     
 
  }

public class Main {
  
       /**
        * @param args
        */
       public static void main(String[] args)
       {
          
           //Lets create nodes as given as an example in the article
           Node nA=new Node('A');
           Node nB=new Node('B');
           Node nC=new Node('C');
           Node nD=new Node('D');
           Node nE=new Node('E');
           Node nF=new Node('F');
  
           //Create the graph, add nodes, create edges between nodes
           Graph g=new Graph();
           g.addNode(nA);
           g.addNode(nB);
           g.addNode(nC);
           g.addNode(nD);
           g.addNode(nE);
           g.addNode(nF);
           g.setRootNode(nA);
          
           g.connectNode(nA,nB);
           g.connectNode(nA,nC);
           g.connectNode(nA,nD);
          
           g.connectNode(nB,nE);
           g.connectNode(nB,nF);
           g.connectNode(nC,nF);
          
          
           //Perform the traversal of the graph
           System.out.println("DFS Traversal of a tree is ------------->");
           g.dfs();
          
           System.out.println("\nBFS Traversal of a tree is ------------->");
           g.bfs();
          
          
          
          
       }
  
 }

   




Time Complexity O(M+N)m is no od edges & n no of nodes in case of connected graph
is will be O(M).
Space Complexity Depends on Implementation if Adjency matrix is Used then it will be O(MN)
else if adjency list is used then it will be equals to number of adjecent nodes of each node. it will O(M+N)

Application of BFS:
1.Finding Connected Components in Graph.
2.Check Graph is Bipartite or Not.
3.Finding interesting web pages (expanding from 
links). Breadth-first works very nicely and quickly 
finds pages with high PageRank R(p). PageRank 
is the scoring measure used by Google.
k is an index over all pages that link to page p; 
C(k) is the total number of links out of k;
R(k) is the PageRank for page k;
T is the total number of web pages on the internet;
d is a number 0 < d < 1.

Application of DFS
1.2-Edge Connectivity in Graph.
2. 2-node connectivity in graph.
3. Check Grap0h is planer or not.
4. solving Puzzles like mouse in the maze