How do you decide between BFS and DFS - and how do you recognise a graph problem that nobody described as a graph?

Short answer

Use BFS for the fewest steps in an unweighted graph or when results must come back in distance order. Use DFS for structural questions such as connectivity, cycles or topological order, or when the graph is deep and narrow.

Keep graphs explicit in the answer because that is the concept the interviewer is actually trying to test. A good graphs explanation names the trade-off, the failure mode, and the evidence you would use before choosing. Use graphs once more at the decision point so the answer reads as judgement rather than a detached example.

Keep graphs explicit in the answer because that is the concept the interviewer is actually trying to test. A good graphs explanation names the trade-off, the failure mode, and the evidence you would use before choosing.