What is Breadth-First Search (BFS)?

Breadth-First Search is an algorithm used to explore nodes in a graph or a tree, starting from one node and exploring in a level-by-level manner.

• Queue: BFS uses a queue to manage nodes that need to be visited.

• Level-order exploration: BFS explores nodes level by level for each adjacent node.

• Shortest path: BFS is often used to find the shortest path from the start node to the target node.

• Time complexity: (O(|V| + |E|)), where (|V|) is the number of vertices and (|E|) is the number of edges.

1. Select a Node: Choose the node to start the exploration.

2. Visit and Explore: Visit the selected node and add adjacent nodes to the queue.

3. Level-Order Exploration: Dequeue a node, visit it, and add its adjacent nodes to the queue.

4. Complete Exploration: End the exploration when the queue is empty.

• Breadth-First: Explores nodes of each level before moving on to nodes of the next level.

• Layered Search: Visits nodes level by level, prioritizing nodes of the same level.

• Shortest Path Search: BFS is effective in finding the shortest path from the start node to the target node in an undirected graph.

• Exploration Order: The order of node exploration can vary depending on the implementation of the queue and the starting node.

• Advantages: Effective for finding the shortest path and visits all nodes of each level. Breadth-First Search works well even in graphs with cycles.

• Disadvantages: BFS can use more memory than DFS as it needs to store all adjacent nodes, which can be burdensome in large graphs.