Breadth First Search algorithm(BFS) traverses a graph in a breadth wards motion and uses a queue to remember to get the next vertex to start a search when a dead end occurs in any iteration. The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array. For simplicity, it is assumed that all vertices are reachable from the starting vertex.
For example, in the following graph, we start traversal from vertex 2. When we come to vertex 0, we look for all adjacent vertices of it. 2 is also an adjacent vertex of 0. If we don’t mark visited vertices, then 2 will be processed again and it will become a non-terminating process. A Breadth First Traversal of the following graph is 2, 0, 3, 1. It employs following rules. Rule 1 − Visit adjacent unvisited vertex. Mark it visited. Display it. Insert it in a queue. Rule 2 − If no adjacent vertex found, remove the first vertex from queue. Rule 3 − Repeat Rule 1 and Rule 2 until queue is empty. At this stage we are left with no unmarked (unvisited) nodes. But as per algorithm we keep on dequeuing in order to get all unvisited nodes. When the queue gets emptied the program is over.
Graph Implementation: import java.util.Iterator; import java.util.LinkedList; /** * */ /** * @author Abhinaw.Tripathi * */ public class Graph { private int V; private LinkedList<Integer> adjacentList[]; Graph(int v) { V = v; adjacentList = new LinkedList[v]; for (int i=0; i<v; ++i) adjacentList[i] = new LinkedList(); } // Function to add an edge into the graph void addEdge(int v,int w) { adjacentList[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 current 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 = adjacentList[s].listIterator(); while (i.hasNext()) { int n = i.next(); if (!visited[n]) { visited[n] = true; queue.add(n); } } } } public static void main(String[] args) { Graph g = new Graph(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); } }
Result:
Following is Breadth First Traversal (starting from vertex 2)
2 0 3 1
Note that the above code traverses only the vertices reachable from a given source vertex. All the vertices may not be reachable from a given vertex (example Disconnected graph). To print all the vertices, we can modify the BFS function to do traversal starting from all nodes one by one .
Time Complexity: O(V+E) where V is number of vertices in the graph and E is number of edges in the graph.