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Breadth First Traversal or BFS for a Graph

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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.

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Following are C++ and Java implementations of simple Breadth First Traversal from a given source.

The C++ implementation uses adjacency list representation of graphs. STL‘s list container is used to store lists of adjacent nodes and queue of nodes needed for BFS traversal.

  • C++
  • Java
  • Python

// 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 representation

class Graph

{

    int V;    // No. of vertices

    list<int> *adj;    // Pointer to an array containing adjacency lists

public:

    Graph(int V);  // Constructor

    void addEdge(int v, int w); // function to add an edge to graph

    void BFS(int s);  // prints BFS traversal from a given source 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 class

int 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;

}

asked Jul 12 in C program by anonymous

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