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# Breadth First Search Algorithm Assignment Help

Breadth-first search (BFS) is a general technique for traversing a graph.

Breadth first search (BFS) is an organized way of visiting vertices as well as edges in a graph. Graph G along with a particular vertex s, the BFS searches through those vertices adjacent to s, after that searches the actual vertices next to individuals vertices, and so on. The routine stops whenever BFS has visited all vertices which are obtainable from s. The phenomenon how the vertices nearest towards the source s are visited earlier in the search process provides this particular search its name. Several procedures could be executed whenever visiting a vertex.

The function BFS in Algorithm1 adopts two of the most frequently utilized procedures:

• Building a breadth-first tree and
• Calculating the distance,
• This is the minimum length of a path, from the source s to each reachable vertex.

## Breadth First Search – Code

### Problem:

• Find length associated with shortest path from s in order to every node,
• Let u.d signify length associated with shortest path through nodes to node u
• Remember: length is number of edges through s to u

### Breadth First Search Algorithm Code:

BFS(V, E, s)
--  Initialize all nodes as unvisited
for each node u loop
u.d:= -1
end loop
-- Mark first node as seen
-- What does the value 0 represent?
-- Put first node on queue of nodes to visit
s.d :=0
enqueue (Q, s)

-- While there are more nodes to visit
while not ismpty(Q) loop
U := dequeue(Q) – dequeues and returns front

-- Process vertex u, as needed
for each vertex v adjacent to u loop
--  Process edge (u, v), as needed
if v.d =-1 then -- Not yet visited
v.d := u.d+1 -- How many times node?
enqueue(Q,v)
end if
end loop

end loop


### Properties:

Notation: Gs (connected component of s)

Property 1: BFS (G, s) visits all the vertices and edges of Gs

Property 2: The discovery edges labeled by BFS (G, s) form a spanning tree Ts of Gs

Property 3: For each vertex ‘v’ in Li. The path of Ts from‘s’ to ‘v’ has ‘i’ edges and every path from‘s’ to ‘v’ in Gs has at least ‘i’ edges

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