Which statement about graph traversal algorithm breadth-first search (BFS) is true?

• A. DFS explores level by level and is useful for shortest paths.
• B. BFS explores as deep as possible.
• C. BFS does not guarantee shortest paths.
• D. BFS explores the graph level by level and is useful for shortest paths in unweighted graphs.

Answer: (D)

BFS works by expanding the search level by level, using a queue to process all nodes at distance k from the start before moving to distance k+1. This level-by-level growth means the first time you reach a node, you’ve followed the smallest possible number of edges from the start, so BFS yields the shortest path in terms edge count for unweighted graphs. In graphs with weights, that guarantee doesn’t apply unless all weights are equal, in which case BFS behaves like it’s operating on an unweighted graph. The other descriptions miss this level-wise behavior or mix BFS up with depth-first search, which goes deep before backtracking and does not guarantee shortest paths.