BFS

Breadth-First Search (BFS) is a graph traversal algorithm that explores nodes level-by-level, visiting all neighbor nodes at the current depth before moving deeper. It employs a FIFO Queue to orchestrate vertex traversal. BFS is guaranteed to discover the shortest path in unweighted graphs.

Complexity Profile

Case	Complexity
Best Case	O(V + E)
Average Case	O(V + E)
Worst Case	O(V + E)
Space Complexity	O(V)

Code Implementation

from collections import deque

def breadth_first_search(graph, start_node):
    visited = set()
    queue = deque([start_node])
    visited.add(start_node)
    
    while queue:
        current = queue.popleft()  # Dequeue
        print("Visited node:", current)
        
        for neighbor in graph.get(current, []):
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append(neighbor)  # Enqueue

Real-World Applications

• Finding shortest path in unweighted networks.
• Social network analysis (finding friends within degrees of connection).
• Web crawlers indexing local links level by level.