CS8391-Data Structures Unit 4
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Breadth first traversal (BFS) is a graph traversal algorithm that begins at a starting node and explores all neighboring nodes at the present distance from the node before proceeding to nodes at the next distance. It uses a queue to keep track of nodes to visit at each level. The key steps are to enqueue the starting node, dequeue nodes and enqueue any unvisited neighbors, repeating until the queue is empty. BFS can be used to check if a graph is connected or not. Depth first search (DFS) recursively explores as far as possible along each branch before backtracking. It involves marking the starting node visited, recursively searching adjacent unvisited nodes, and marking nodes visited along the way.
![Void BFS(vertex u)
{
initialize queue Q;
visited[u]=1;
enqueue(u,Q);
while(!isempty)
{
u= Dequeue(Q)
print u
for all vertices v adjacent to u do
if (visited[v]==0) then
{
Enqueue(v,Q)
visited[v]=1;
}
}
}](https://image.slidesharecdn.com/unitiv-210524101229/85/CS8391-Data-Structures-Unit-4-4-320.jpg)
![Routine for DFS
Void DFS(Vertex V)
{
visited[V]=True;
for each W adjacent to V
if (! Visited[W])
DFS(W);
}](https://image.slidesharecdn.com/unitiv-210524101229/85/CS8391-Data-Structures-Unit-4-8-320.jpg)
CS8391-Data Structures Unit 4
- 1. Graph traversal •A graph traversal is a systematic way of visiting the nodes in a specific order •Types •Depth first traversal •Breadth first traversal
- 2. Breadth first traversal(BFS) • Graph G starts from an unvisited vertex u • Then all unvisited vertices vi adjacent to u are visited and then all unvisited vertices wj adjacent to vj are visited and so on
- 3. • Choose any node in the graph designate it as the search node & mark it as visited • Using the adjacency matrix of the graph, find all the unvisited adjacent nodes to the search node and enqueue them into the queue Q • Then the search node is dequeued from the queue. Mark that node as visited and select the new search node • Repeat step 2 & 3 using the new search node
- 4. Void BFS(vertex u) { initialize queue Q; visited[u]=1; enqueue(u,Q); while(!isempty) { u= Dequeue(Q) print u for all vertices v adjacent to u do if (visited[v]==0) then { Enqueue(v,Q) visited[v]=1; } } }
- 5. applications • To check whether the graph is connected or not
- 6. Depth first search • Depth first search works by selecting one vertex V of G as a start vertex • V is marked visited • Then each unvisited vertex adjacent to V is searched using depth first search recursively • This process continues until a dead end / no adjacent unvisited vertices is encountered
- 7. 1. Choose any node in the graph. Designate it as the search node and mark it as visited 2. Using the adjacency matrix of the graph, find a node adjacent to the search node that has not been visited yet. Designate this as the new search node and mark it as visited. 3. Repeat step 1 & 2 using the new search node
- 8. Routine for DFS Void DFS(Vertex V) { visited[V]=True; for each W adjacent to V if (! Visited[W]) DFS(W); }