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BFS using vectors & queue as per the algorithm of CLRS

Breadth-first search traversal of a graph using the algorithm given in CLRS book.

BFS is one of the ways to traverse a graph. It is named so because it expands the frontier between discovered and undiscovered vertices uniformly across the breadth of the frontier. What it means is that the algorithm first discovers all the vertices connected to “u” at a distance of k before discovering the vertices at a distance of k+1 from u. The algorithm given in CLRS uses the concept of “colour” to check if a vertex is discovered fully or partially or undiscovered. It also keeps a track of the distance a vertex u is from the source s.

BFS(G,s)
1  for each vertex u in G.V - {s}
2     u.color = white
3     u.d = INF
4     u.p = NIL
5  s.color = green
6  s.d = 0
7  s.p = NIL
8  Q = NULL
9  ENQUEUE(Q,s)
10 while Q != NULL
11    u = DEQUEUE(Q)
12    for each v in G.Adj[u]
13       if v.color == white
14          v.color = green
15          v.d = u.d + 1
16          v.p = u
17          ENQUEUE(Q,v)
18    u.color = dark_green

It produces a “breadth-first tree” with root s that contains all reachable vertices. Let’s take a simple directed graph and see how BFS traverses it.

The graph


Starting of traversal


1st traversal


1st traversal completes



C++

// CPP program to implement BFS as per CLRS 
// algorithm.
#include <bits/stdc++.h>
using namespace std;
  
// Declaring the vectors to store color, distance
// and parent
vector<string> colour;
vector<int> d;
vector<int> p;
  
/* This function adds an edge to the graph.
It is an undirected graph. So edges are 
added for both the nodes. */
void addEdge(vector <int> g[], int u, int v)
{
    g[u].push_back(v);
    g[v].push_back(u);
}
  
/* This function does the Breadth First Search*/
void BFSSingleSource(vector <int> g[], int s)
{
    // The Queue used for the BFS operation
    queue<int> q;
  
    // Pushing the root node inside the queue
    q.push(s); 
  
    /* Distance of root node is 0 & colour
    is gray as it is visited partially now */
    d[s] = 0;
    colour[s] = "green";
          
    /* Loop to traverse the graph. Traversal
    will happen traverse until the queue is 
    not empty.*/
    while (!q.empty())
    {
        /* Extracting the front element(node) 
        and poping it out of queue. */
        int u = q.front();
        q.pop();
  
        cout << u << " ";
  
        /* This loop traverses all the child nodes of u */
        for (auto i = g[u].begin(); i != g[u].end(); i++)
        {
            /* If the colour is white then the said node
            is not traversed. */
            if (colour[*i] == "white")
            {
                colour[*i] = "green";
                d[*i] = d[u] + 1;
                p[*i] = u;
  
                /* Pushing the node inside queue
                to traverse its children. */
                q.push(*i); 
            }
        }
  
        /* Now the node u is completely traversed
        and colour is changed to black. */
        colour[u] = "dark_green";
    }
}
  
void BFSFull(vector <int> g[], int n)
{
    /* Initially all nodes are not traversed.
    Therefore, the colour is white. */
    colour.assign(n, "white");
    d.assign(n, 0);
    p.assign(n, -1);
  
    // Calling BFSSingleSource() for all white
    // vertices.
    for (int i = 0; i < n; i++)     
        if (colour[i] == "white")
            BFSSingleSource(g, i); 
}
  
// Driver Function
int main()
{
    // Graph with 7 nodes and 6 edges.
    int n = 7;
          
    // The Graph vector
    vector <int> g[n];
      
    addEdge(g, 0, 1);
    addEdge(g, 0, 2);
    addEdge(g, 1, 3);
    addEdge(g, 1, 4);
    addEdge(g, 2, 5);
    addEdge(g, 2, 6);
  
    BFSFull(g, n);
  
    return 0;
}

Python3

# Python3 program to implement BFS as
# per CLRS algorithm.
import queue

# This function adds an edge to the graph.
# It is an undirected graph. So edges
# are added for both the nodes.
def addEdge(g, u, v):
g[u].append(v)
g[v].append(u)

# This function does the Breadth
# First Search
def BFSSingleSource(g, s):

# The Queue used for the BFS operation
q = queue.Queue()

# Pushing the root node inside
# the queue
q.put(s)

# Distance of root node is 0 & colour is
# gray as it is visited partially now
d[s] = 0
colour[s] = “green”

# Loop to traverse the graph. Traversal
# will happen traverse until the queue
# is not empty.
while (not q.empty()):

# Extracting the front element(node)
# and poping it out of queue.
u = q.get()

print(u, end = ” “)

# This loop traverses all the child
# nodes of u
i = 0
while i < len(g[u]): # If the colour is white then # the said node is not traversed. if (colour[g[u][i]] == "white"): colour[g[u][i]] = "green" d[g[u][i]] = d[u] + 1 p[g[u][i]] = u # Pushing the node inside queue # to traverse its children. q.put(g[u][i]) i += 1 # Now the node u is completely traversed # and colour is changed to black. colour[u] = "dark_green" def BFSFull(g, n): # Initially all nodes are not traversed. # Therefore, the colour is white. colour = ["white"] * n d = [0] * n p = [-1] * n # Calling BFSSingleSource() for all # white vertices for i in range(n): if (colour[i] == "white"): BFSSingleSource(g, i) # Driver Code # Graph with 7 nodes and 6 edges. n = 7 # Declaring the vectors to store color, # distance and parent colour = [None] * n d = [None] * n p = [None] * n # The Graph vector g = [[] for i in range(n)] addEdge(g, 0, 1) addEdge(g, 0, 2) addEdge(g, 1, 3) addEdge(g, 1, 4) addEdge(g, 2, 5) addEdge(g, 2, 6) BFSFull(g, n) # This code is contributed by Pranchalk [tabbyending] Output:

0 1 2 3 4 5 6


This article is attributed to GeeksforGeeks.org

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