Introduction
Breadth-First Search (BFS): BFS is a graph traversal algorithm used to explore nodes and edges of a graph systematically. It starts at a given source node and explores all its neighbors before moving to the next level of neighbors.
BFS is widely used in various applications, such as finding the shortest path in an unweighted graph and solving puzzles like mazes.
How does it work?
- Start from the source node and mark it as visited.
- Use a queue to keep track of nodes to be explored.
- Dequeue a node, process it, and enqueue all its unvisited neighbors.
- Repeat the process until the queue is empty.
Important Observations
- BFS explores all nodes at the current depth level before moving to the next level.
- It guarantees the shortest path in an unweighted graph.
- It uses a queue to manage the traversal order.
Key Characteristics:
- Level-order traversal of graph nodes.
- Suitable for both connected and disconnected graphs.
- Works for both directed and undirected graphs.
Advantages:
- Simple and easy to implement.
- Finds the shortest path in an unweighted graph.
- Can detect connected components in a graph.
Disadvantages:
- Consumes more memory due to the use of a queue.
- Not suitable for weighted graphs (use Dijkstra's algorithm instead).
Time Complexity:
- For adjacency list representation: O(V + E), where V is the number of vertices and E is the number of edges.
- For adjacency matrix representation: O(V2).