Breadth-First Search, or BFS, is a fundamental graph traversal algorithm. It explores nodes level by level, starting from a root node and visiting all neighbors at the current depth before moving to the next level. BFS uses a queue data structure and guarantees the shortest path in unweighted graphs.
Let's walk through the BFS algorithm step by step. We start with node A as our root. First, we add A to the queue and mark it as visited. Then we dequeue A and visit its neighbors B and C, adding them to the queue. Next, we dequeue B and visit its unvisited neighbors D and E. We continue this process until the queue becomes empty.
Here's the implementation of BFS in Python. The algorithm uses a queue for FIFO processing, a visited set to track explored nodes, and a result list to store the traversal order. We start by adding the starting node to the queue, then repeatedly dequeue nodes, mark them as visited, and add their unvisited neighbors to the queue.
BFS has many practical applications. It finds the shortest path in unweighted graphs, performs level-order tree traversal, analyzes social networks, and enables web crawling. The algorithm has O(V plus E) time complexity and O(V) space complexity. It's complete and optimal for unweighted graphs, making it ideal for pathfinding problems like maze solving.
To summarize what we've learned about Breadth-First Search: BFS is a fundamental graph traversal algorithm that explores nodes level by level using a queue data structure. It guarantees the shortest path in unweighted graphs and has efficient O(V plus E) time complexity. BFS is widely used in pathfinding, network analysis, and many other computer science applications.