Búsqueda primero en amplitud o BFS para un gráfico

El recorrido primero en amplitud (o búsqueda) para un gráfico es similar al recorrido primero en amplitud de un árbol (consulte el método 2 de esta publicación ). El único problema aquí es que, a diferencia de los árboles, los gráficos pueden contener ciclos, por lo que podemos volver al mismo Node. Para evitar procesar un Node más de una vez, usamos una array visitada booleana. Para simplificar, se supone que todos los vértices son accesibles desde el vértice inicial. BFS utiliza una estructura de datos de cola para el cruce.

Por ejemplo, en el siguiente gráfico, comenzamos el recorrido desde el vértice 2. Cuando llegamos al vértice 0, buscamos todos los vértices adyacentes. 2 también es un vértice adyacente de 0. Si no marcamos los vértices visitados, entonces 2 se procesará nuevamente y se convertirá en un proceso sin terminación. 

// Program to print BFS traversal from a given
// source vertex. BFS(int s) traverses vertices
// reachable from s.
#include<bits/stdc++.h>
using namespace std;
 
// This class represents a directed graph using
// adjacency list representation
class Graph
{
    int V;    // No. of vertices
 
    // Pointer to an array containing adjacency
    // lists
    vector<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.resize(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
    vector<bool> visited;
    visited.resize(V,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);
 
    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 (auto adjecent: adj[s])
        {
            if (!visited[adjecent])
            {
                visited[adjecent] = true;
                queue.push_back(adjecent);
            }
        }
    }
}
 
// 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;
}

// 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
// representation
class 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 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 representation
class 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 diagram
g = 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# 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 code
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);
     
    Console.Write("Following is Breadth First " +
                  "Traversal(starting from " +
                  "vertex 2)\n");
    g.BFS(2);
}
}
 
// This code is contributed by anv89

/*******************************************************
 * Generic Function for BFS traversal of a Graph
 * (valid for directed as well as undirected graphs
 *  which can have multiple disconnected commponents)
 *
 ********** Inputs *************************************
 * V - represents number of vertices in the Graph
 * adj[] - represents adjacency list for the Graph
 *
 ********** Output *************************************
 * bfs_traversal - a vector containing bfs traversal
 *                 for entire graph
 *******************************************************/
 
vector<int> bfsOfGraph(int V, vector<int> adj[])
{
    vector<int> bfs_traversal;
    vector<bool> vis(V, false);
    for (int i = 0; i < V; ++i) {
        if (!vis[i]) {
            queue<int> q;
            vis[i] = true;
            q.push(i);
            while (!q.empty()) {
                int g_node = q.front();
                q.pop();
                bfs_traversal.push_back(g_node);
                for (auto it : adj[g_node]) {
                    if (!vis[it]) {
                        vis[it] = true;
                        q.push(it);
                    }
                }
            }
        }
    }
    return bfs_traversal;
}