Breadth First Search or BFS for a Graph
Breadth-First Traversal (or Search) for a graph is similar to Breadth-First Traversal of a tree (See method 2 of this post). 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.
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Following are the implementations of simple Breadth-First Traversal from a given source.
The implementation uses an adjacency list representation of graphs. STL‘s list container is used to store lists of adjacent nodes and the queue of nodes needed for BFS traversal.
C++
// Program to print BFS traversal from a given// source vertex. BFS(int s) traverses vertices // reachable from s.#include<iostream>#include <list>using namespace std;// This class represents a directed graph using// adjacency list representationclass Graph{ int V; // No. of vertices // Pointer to an array containing adjacency // lists list<int> *adj; public: Graph(int V); // Constructor // function to add an edge to graph void addEdge(int v, int w); // prints BFS traversal from a given source s void BFS(int s); };Graph::Graph(int V){ this->V = V; adj = new list<int>[V];}void Graph::addEdge(int v, int w){ adj[v].push_back(w); // Add w to v’s list.}void Graph::BFS(int s){ // Mark all the vertices as not visited bool *visited = new bool[V]; for(int i = 0; i < V; i++) visited[i] = false; // Create a queue for BFS list<int> queue; // Mark the current node as visited and enqueue it visited[s] = true; queue.push_back(s); // 'i' will be used to get all adjacent // vertices of a vertex list<int>::iterator i; while(!queue.empty()) { // Dequeue a vertex from queue and print it s = queue.front(); cout << s << " "; queue.pop_front(); // Get all adjacent vertices of the dequeued // vertex s. If a adjacent has not been visited, // then mark it visited and enqueue it for (i = adj[s].begin(); i != adj[s].end(); ++i) { if (!visited[*i]) { visited[*i] = true; queue.push_back(*i); } } }}// Driver program to test methods of graph classint main(){ // Create a graph given in the above diagram Graph g(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); cout << "Following is Breadth First Traversal " << "(starting from vertex 2) \n"; g.BFS(2); return 0;} |
Java
// Java program to print BFS traversal from a given source vertex.// BFS(int s) traverses vertices reachable from s.import java.io.*;import java.util.*;// This class represents a directed graph using adjacency list// representationclass Graph{ private int V; // No. of vertices private LinkedList<Integer> adj[]; //Adjacency Lists // Constructor Graph(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 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 = 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[]) { 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); }}// This code is contributed by Aakash Hasija |
Python3
# Python3 Program to print BFS traversal# from a given source vertex. BFS(int s)# traverses vertices reachable from s.from collections import defaultdict# This class represents a directed graph# using adjacency list representationclass Graph: # Constructor def __init__(self): # default dictionary to store graph self.graph = defaultdict(list) # function to add an edge to graph def addEdge(self,u,v): self.graph[u].append(v) # Function to print a BFS of graph def BFS(self, s): # Mark all the vertices as not visited visited = [False] * (max(self.graph) + 1) # Create a queue for BFS queue = [] # Mark the source node as # visited and enqueue it queue.append(s) visited[s] = True while queue: # Dequeue a vertex from # queue and print it s = queue.pop(0) print (s, end = " ") # Get all adjacent vertices of the # dequeued vertex s. If a adjacent # has not been visited, then mark it # visited and enqueue it for i in self.graph[s]: if visited[i] == False: queue.append(i) visited[i] = True# Driver code# Create a graph given in# the above diagramg = Graph()g.addEdge(0, 1)g.addEdge(0, 2)g.addEdge(1, 2)g.addEdge(2, 0)g.addEdge(2, 3)g.addEdge(3, 3)print ("Following is Breadth First Traversal" " (starting from vertex 2)")g.BFS(2)# This code is contributed by Neelam Yadav |
C#
// C# program to print BFS traversal // from a given source vertex. // BFS(int s) traverses vertices // reachable from s. using System;using System.Collections.Generic;using System.Linq;using System.Text;// This class represents a directed // graph using adjacency list // representation class Graph{ // No. of vertices private int _V; //Adjacency Lists LinkedList<int>[] _adj; public Graph(int V){ _adj = new LinkedList<int>[V]; for(int i = 0; i < _adj.Length; i++) { _adj[i] = new LinkedList<int>(); } _V = V;}// Function to add an edge into the graph public void AddEdge(int v, int w){ _adj[v].AddLast(w);}// Prints BFS traversal from a given source s public void BFS(int s){ // Mark all the vertices as not // visited(By default set as false) bool[] visited = new bool[_V]; for(int i = 0; i < _V; i++) visited[i] = false; // Create a queue for BFS LinkedList<int> queue = new LinkedList<int>(); // Mark the current node as // visited and enqueue it visited[s] = true; queue.AddLast(s); while(queue.Any()) { // Dequeue a vertex from queue // and print it s = queue.First(); Console.Write(s + " " ); queue.RemoveFirst(); // Get all adjacent vertices of the // dequeued vertex s. If a adjacent // has not been visited, then mark it // visited and enqueue it LinkedList<int> list = _adj[s]; foreach (var val in list) { if (!visited[val]) { visited[val] = true; queue.AddLast(val); } } }}// Driver codestatic 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); Console.Write("Following is Breadth First " + "Traversal(starting from " + "vertex 2)\n"); g.BFS(2);}}// This code is contributed by anv89 |
Output:
Following is Breadth First Traversal (starting from vertex 2) 2 0 3 1
Illustration :
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 (for example Disconnected graph). To print all the vertices, we can modify the BFS function to do traversal starting from all nodes one by one (Like the DFS modified version).
Time Complexity: O(V+E) where V is a number of vertices in the graph and E is a number of edges in the graph.
https://youtu.be/0u78hx-66Xk
You may like to see below also :
- Recent Articles on BFS
- Depth First Traversal
- Applications of Breadth First Traversal
- Applications of Depth First Search
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