- Explain the Breadth-First Search (BFS) algorithm. Provide an example. explain the answer for 5 marks

Breadth-First Search (BFS) is a graph traversal algorithm that explores all the vertices of a graph in breadth-first order, i.e., it explores all the vertices at the present depth before moving on to vertices at the next depth level. It uses a queue data structure to keep track of vertices to be explored.

Here are the steps of the BFS algorithm:

1. Start by picking any node, preferably the root if it is a tree. Mark this node as visited and enqueue it into the queue.

2. Dequeue a vertex from the queue. Let's call this vertex, 'v'.

3. Visit all the unvisited neighbors of 'v', mark them as visited, and enqueue them into the queue.

4. Repeat steps 2 and 3 until the queue is empty.

Example:

Consider the following graph:

  1
 / \
2   3
   / \
  4   5

We start from vertex 1, the BFS algorithm starts by going to each neighbor, so it first visits 2 and 3, and then it goes to visit the neighbors of 2 and 3 which are 4 and 5. So the output of the BFS traversal of the above graph is 1, 2, 3, 4, 5.

This algorithm is particularly useful for finding the shortest path in unweighted graphs or for any scenario where all the edges have the same weight.