![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](https://image.slidesharecdn.com/ada-191015145338/85/Breadth-First-Search-BFS-7-320.jpg)
Breadth First Search (BFS)
- 1. WELCOME Name: Dhrumil I. Panchal Enrollment No.: 170410107053 Subject: Analysis and Design of Algorithms Branch: Computer Engineering (B.E.) Year: 2019-20
- 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