Breadth First-Search

Lecturer: Miss Sana Rizwan

Muhammad Arslan KhanDDP-FA12-BSE-072

Mutasadiq IqbalDDP-FA12-BSE-072

Section: C

Presented By

Breadth-first search (BFS) start from the root node and explores all the neighbouring nodes. Then for each of those nearest nodes, it explores their neighbour nodes, and so on, until it finds the goal.

Definition

Breadth-first search can be used to solve many problems in graph theory, for example:

• Finding all nodes within one connected components.• Finding the shortest path between two nodes u and v .• Testing a graph for bipartiteness.

Applications

•  Undiscovered--white colour

• Discovered but not fully explored-grey colour

• Fully explored.-black colour

States

• Pick a source vertex S to start.• Find (or discover) the vertices that are adjacent to S.• Pick each child of S in turn and discover their vertices adjacent to that

child.• Done when all children have been discovered and examined.• The breadth-first search uses a FIFO queue.

How It Works?

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Algorithm

Algorithm BFS(s )1. color all the vertices white2. initialize an empty queue Q3. for each neighbor v of s4. insert v in Q ; color [v ] = grey5. output s ; color [s ] = black6. while Q is not empty7. u = top of Q ; remove u from Q8. for each neighbor v of u9. if color [v ] = white10. insert v in Q ; color [v ] = grey11. output u; color [u] = black