This document discusses breadth-first search (BFS), an algorithm for exploring the vertices of a graph. It begins with an introduction to BFS, explaining that it systematically explores the edges of a graph to discover every reachable vertex from a source vertex s, computing the distance from s to each vertex. It then provides pseudocode for the BFS algorithm and notes that BFS works on both directed and undirected graphs, discovering all vertices at a given distance k from s before moving to distance k+1. An example of running BFS on a graph is referenced but not shown.

1. WELCOME
Name: Dhrumil I. Panchal
Enrollment No.: 170410107053
Subject: Analysis and Design of Algorithms
Branch: Computer Engineering (B.E.)
Year: 2019-20

2. TOPIC
Breadth-First Search

3. CONTAIN
Introduction
Algorithm
Example

4. BFS
 Given a graph G = (V, E) and a distinguished source vertex s, breadth-
first search systematically explores the edges of G to "discover" every
vertex that is reachable from s.
 It computes the distance (smallest number of edges) from s to each
reachable vertex.
 It also produces a "breadth-first tree" with root s that contains all
reachable vertices.
 For any vertex v reachable from s, the path in the breadth-first tree
from s to v corresponds to a "shortest path" from s to v in G, that is, a
path containing the smallest number of edges.

5. CONTI…
The algorithm works on both directed and undirected graphs.
Breadth-first search is so named because it expands the frontier
between discovered and undiscovered vertices uniformly across
the breadth of the frontier.
That is, the algorithm discovers all vertices at distance k from s
before discovering any vertices at distance k + 1.

6. BFS (G, S)
for each vertex u ϵ G.V – {s}
u.color = WHITE
u.d = ∞
u.π = NIL
s.color = GRAY
s.d = 0
s. π = NIL
Q = Ø
ENQUEUE (Q, s)

7. BFS (G, S)
while Q != Ø
u = DEQUEUE (Q)
for each v ϵ G.adj[u]
if v.color == WHITE
v.color = GRAY
v.d = u.d + 1
v. π = u
ENQUEUE (Q, v)
u.color = BLACK

8. CONTI…
Breadth first search in not naturally recursive. To understand the
differences and similarities, let us first consider the non-recursive
formulation of DFS algorithm.
Let stack be a data type allowing two operations PUSH and POP.
It handles elements in LIFO odder.
The function top denotes the first element at the top of the stack.

9. EXAMPLE

10. IF NODE 1 IS STARTING POINT

11. REFERENCES
Inspiration from Prof. Jayna B. Shah
Notes of ADA
Textbook of ADA
Images from Google Images
Some my own Knowledge

12. THANK YOU