Breadth-First Search, or BFS, is a fundamental graph traversal algorithm. It explores nodes in a graph systematically, visiting all neighbors at the current depth level before moving to nodes at the next depth level. This layer-by-layer approach makes BFS particularly useful for finding shortest paths in unweighted graphs.
The BFS algorithm follows a systematic approach. First, we initialize by marking the source node as visited and adding it to a queue. Then, while the queue is not empty, we dequeue the front node and process it. For each unvisited neighbor of the current node, we mark it as visited and add it to the queue. This process continues until the queue becomes empty, ensuring all reachable nodes are visited.
Let's trace through a BFS execution starting from node A. At level 0, we have only node A. At level 1, we visit A's neighbors: B and D. At level 2, we visit the unvisited neighbors of B and D, which are C and E. The complete visit order is A, then B, then D, then C, and finally E. This demonstrates how BFS explores the graph layer by layer.
Here's a simple BFS implementation in Python. The algorithm uses a queue to store nodes to visit and a set to track visited nodes. The time complexity is O of V plus E, where V is the number of vertices and E is the number of edges. The space complexity is O of V for storing the visited set and queue. BFS is commonly used for finding shortest paths in unweighted graphs, level-order traversal of trees, finding connected components, and web crawling applications.
To summarize what we've learned about BFS: It's a fundamental graph traversal algorithm that explores nodes level by level using a queue data structure. BFS guarantees finding the shortest path in unweighted graphs. It has linear time complexity and is essential for many applications in computer science including pathfinding and graph analysis.