Breadth First Search ( BFS )

Graph and tree traversal using Breadth First Search (BFS) algorithm

Breadth First Search (BFS) is an algorithm for traversing an unweighted Graph or a Tree. BFS starts with the root node and explores each adjacent node before exploring node(s) at the next level. BFS makes use of Queue for storing the visited nodes of the graph / tree.

Example: Consider the below step-by-step BFS traversal of the tree. If the source is root (node ‘0’), the immediately connected nodes ‘1’ & ‘2’ are considered at the same level and are explored before the other nodes in the tree.

BFS_Example_Run


Algorithm : Breadth first search (Graph G, Souce_Vertex S)

1.    Create a queue Q to store the vertices.
2.    Push the source vertex S in the queue Q.
3.    Mark S as visited.
4.    While the queue Q is not empty
5.        Remove vertex U from the front of the queue. i.e Vertex U = Q.front(), Q.pop()
6.        For every vertex V adjacent to the vertex U
7.            If the vertex V is not visited
8.               Explore the vertex V and mark V as visited.
9.               Push the vertex V in the queue Q.


Example of breadth-first search traversal on a graph : In the below unweighted graph, the BFS algorithm beings by exploring node ‘0’ and its adjacent vertices (node ‘1’ and node ‘2’) before exploring node ‘3’ which is at the next level.

BFS_Graph

Example of breadth-first search traversal on a tree : In the below tree, the BFS algorithm beings by exploring node ‘0’ and its adjacent vertices (node ‘1’, ‘2’ and ‘3’) before exploring node ‘4’ which is at the next level.
BFS_Tree

Data structure used for storing graph : Adjacency list
Data structure used for breadth first search : Queue
Time complexity of breadth first search : O(V+E) for an adjacency list implementation of a graph. ‘V’ is the number of vertices and ‘E’ is the number of edges in a graph.


Python

Python program for traversing a graph / tree using Breadth First Search (BFS) algorithm.


Java

Java program for traversing a graph / tree using Breadth First Search (BFS) algorithm.


C++ program for traversing a graph / tree using Breadth First Search (BFS) algorithm.

#include<iostream>
#include<list>
#include<queue>
#include<vector>

using namespace std;

class Graph {

    private:
        int vertices;
        list<int> *adjlist;
        vector<bool> visited;
    public:
        Graph () {
        }

        Graph (int nodes) { 
            adjlist = new list<int> [nodes];
            visited.resize(nodes, false);  
            vertices = nodes;
        }

        ~Graph () { 
            delete [] adjlist;
        }

        void AddEdge (int src, int dst) {
            adjlist[src].push_back(dst);
            adjlist[dst].push_back(src);
        }
    
        void BFS (int source) {

            queue<int> Q;
            visited[source] = true;
            Q.push(source);

            while (!Q.empty()) {

                int node = Q.front();
                Q.pop();
                cout << node << " ";

                for (auto& adj_node : adjlist[node]) {
                    if (!visited[adj_node]) {
                        visited[adj_node] = true;
                        Q.push(adj_node);
                    }
                }
            }
            // Reset the visited array for next iteration of breadth first search
            fill (visited.begin(), visited.end(), false);
        }
};

int main(){
        
    Graph g(7); 

    g.AddEdge(0,1); 
    g.AddEdge(0,2); 
    g.AddEdge(1,3); 
    g.AddEdge(1,4); 
    g.AddEdge(2,3);
    g.AddEdge(3,5); 
    g.AddEdge(4,6); 
    g.AddEdge(5,6); 

    cout << "BFS Graph Traversal" << endl;
    cout << "Source Node(0): "; g.BFS(0); cout << endl;
    cout << "Source Node(3): "; g.BFS(3); cout << endl;

    Graph t(10); 

    t.AddEdge(0,1); 
    t.AddEdge(0,2); 
    t.AddEdge(0,3); 
    t.AddEdge(1,4); 
    t.AddEdge(1,5); 
    t.AddEdge(1,6);
    t.AddEdge(3,7); 
    t.AddEdge(3,8); 
    t.AddEdge(4,9); 

    cout << "BFS Tree Traversal" << endl;
    cout << "Root Node (0): "; t.BFS(0); cout << endl;
    cout << "Root Node (9): "; t.BFS(9); cout << endl;

    return 0;
}

Output of breadth-first search.

BFS Graph Traversal
Source Node(0): 0 1 2 3 4 5 6
Source Node(3): 3 1 2 5 0 4 6

BFS Tree Traversal
Root Node (0): 0 1 2 3 4 5 6 7 8 9
Root Node (9): 9 4 1 0 5 6 2 3 7 8 

Copyright (c) 2019 - 2020, Algotree.org.
All rights reserved.