Word Ladder: BFS for Shortest Transformation

Breadth-First Search is the go-to algorithm for finding shortest paths in unweighted graphs and for level-by-level traversal of trees and graphs. BFS uses a queue to explore all neighbors at the current depth before moving to nodes at the next depth level. This guarantees that the first time we reach a node, we have found the shortest path to it. To implement BFS for this problem, initialize a queue with the starting node and a visited set to avoid processing the same node multiple times. While the queue is not empty, dequeue the front node, process it, and enqueue all its unvisited neighbors. For shortest-path problems, track the distance by incrementing a level counter after processing all nodes at the current depth. Multi-source BFS is a powerful variant where we initialize the queue with multiple starting nodes simultaneously, useful for problems like rotting oranges or walls and gates. The time complexity of BFS is O(V + E) where V is the number of vertices and E is the number of edges. The space complexity is O(V) for the queue and visited set. When working with grid problems, remember that the grid itself serves as the graph, with each cell being a node and edges connecting adjacent cells in four or eight directions.