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

# 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

## leave a comment

## 0 Comments