Breadth First Search - Graph - Java

Breadth First Search (BFS) is a graph traversal algorithm that visits all vertices of a graph in breadth-first order, i.e., it visits all vertices at a certain distance before visiting vertices at a greater distance. Here's the Java code for BFS in an undirected graph:

import java.util.*;

class BFS {
    private int V;   // No. of vertices
    private LinkedList<Integer> adj[]; //Adjacency List

    // Constructor
    BFS(int v) {
        V = v;
        adj = new LinkedList[v];
        for (int i=0; i<v; ++i)
            adj[i] = new LinkedList();
    }

    // Function to add an edge into the graph
    void addEdge(int v,int w) {
        adj[v].add(w);
    }

    // prints BFS traversal from a given source s
    void BFS(int s) {
        // Mark all the vertices as not visited(By default
        // set as false)
        boolean visited[] = new boolean[V];

        // Create a queue for BFS
        LinkedList<Integer> queue = new LinkedList<Integer>();

        // Mark the source node as visited and enqueue it
        visited[s]=true;
        queue.add(s);

        while (queue.size() != 0)
        {
            // Dequeue a vertex from queue and print it
            s = queue.poll();
            System.out.print(s+" ");

            // Get all adjacent vertices of the dequeued vertex s
            // If a adjacent has not been visited, then mark it
            // visited and enqueue it
            Iterator<Integer> i = adj[s].listIterator();
            while (i.hasNext())
            {
                int n = i.next();
                if (!visited[n])
                {
                    visited[n] = true;
                    queue.add(n);
                }
            }
        }
    }

    // Driver method to
    public static void main(String args[])
    {
        BFS g = new BFS(4);

        g.addEdge(0, 1);
        g.addEdge(0, 2);
        g.addEdge(1, 2);
        g.addEdge(2, 0);
        g.addEdge(2, 3);
        g.addEdge(3, 3);

        System.out.println("Following is Breadth First Traversal "+
                           "(starting from vertex 2)");

        g.BFS(2);
    }
}

This code uses an adjacency list to represent the graph, with each index of the list representing a vertex, and the elements in the list representing the vertices adjacent to that vertex. The BFS method implements the BFS algorithm, starting from the source vertex s. It uses a boolean array visited to keep track of which vertices have been visited, and a queue to store the vertices to be visited. The method repeatedly dequeues a vertex from the queue, marks it as visited, and adds its unvisited neighbors to the queue. Here's the sample output for the above code: Following is the output of the code:

Following is Breadth First Traversal (starting from vertex 2)
2 0 3 1

In this example, the graph has 4 vertices and the BFS algorithm is started from vertex 2. The output shows the order in which the vertices were visited during the BFS.

Time complexity of BFS is O(V+E), where V is the number of vertices and E is the number of edges in the graph. This is because in the worst case, all vertices and edges will be visited and processed.

Space complexity of BFS is O(V), where V is the number of vertices in the graph. This is because the space required to store the vertices to be visited in the queue is proportional to the number of vertices.