Lecture 370:- Breadth First Search

Breadth-First Search (BFS) is a graph traversal algorithm used to explore all the vertices of a graph in breadthward motion. It starts at a specified source vertex and explores all its neighbors at the current depth before moving on to the neighbors at the next depth level. BFS is implemented using a queue data structure to keep track of the vertices that need to be visited.

The steps to perform BFS on a graph are as follows:

1. Initialize a queue data structure and a boolean array to keep track of visited vertices.
2. Add the source vertex to the queue and mark it as visited.
3. While the queue is not empty, do the following: a. Dequeue a vertex from the queue and process it. b. Enqueue all the unvisited neighbors of the dequeued vertex and mark them as visited.
4. Repeat step 3 until the queue becomes empty.

BFS ensures that all the vertices at a particular distance from the source vertex are visited before moving on to the vertices at the next distance level. This means that BFS visits all the vertices of the graph and discovers the shortest path to each reachable vertex from the source vertex in an unweighted graph.

BFS is commonly used in many graph-related problems, such as finding connected components, computing shortest paths in unweighted graphs, and solving puzzles like the "Knight's Tour" and "Maze Solving."

The time complexity of BFS is O(V + E), where V is the number of vertices and E is the number of edges in the graph. This is because BFS visits each vertex and each edge exactly once. The space complexity is O(V) as it requires additional space to store the queue and the boolean array to keep track of visited vertices.

BFS is a complete algorithm and guarantees that all vertices will be explored if the graph is connected. It is also optimal for finding the shortest path in an unweighted graph. However, it may not be suitable for graphs with a large number of vertices and edges due to its space and time complexity. For such cases, more efficient algorithms like Dijkstra's algorithm or A* algorithm can be used for weighted graphs.