Final answer:
The four search algorithms discussed—DFS, BFS, greedy best-first search, and A* search with Manhattan distance heuristic—each have their own applications and one cannot be singled out as the sole option without additional problem context. All of these can be used in search problems but have different characteristics that make them suitable for various scenarios.
Step-by-step explanation:
The question asked revolves around four different search algorithms, namely depth-first search (DFS), breadth-first search (BFS), greedy best-first search with Manhattan distance heuristic, and A* search with Manhattan distance heuristic. The inquiry is about identifying which one of them could be used in a given scenario. Without additional context, it's difficult to definitively say which algorithm 'could only be' used as the student asks. However, in theory, any of these algorithms 'could' be used in pathfinding or search problems, depending on the specific requirements and constraints of the problem. DFS explores as far down as possible along each branch before backtracking, which makes it less useful for finding the shortest path but efficient in finding any path. BFS searches level by level and is often used to find the shortest path on unweighted graphs. The greedy best-first search algorithm is a heuristic-based approach that tries to expand the node that appears to be closest to the goal, relying heavily on the heuristic — in this case, the Manhattan distance. A* search, on the other hand, combines aspects of both DFS and BFS, using a heuristic to estimate the total cost of the path through the node and can find the shortest path efficiently if the heuristic is admissible.