My first instinct was Dijkstra but that minimizes, not maximizes, and I lost maybe three minutes mentally fumbling with log transformations before just going with DFS and tracking visited nodes.
Model the problem as a directed graph where currencies are nodes and exchange rates are weighted edges, then find the maximum product path from source to target without revisiting nodes. Use DFS with backtracking to explore all simple paths, or adapt Bellman-Ford for longest path in a DAG if the graph is acyclic; handle duplicate pairs by keeping the highest rate.
Pro tip: Clarify whether the graph can contain cycles and whether the problem guarantees a path; if cycles exist, mention that the longest path problem is NP-hard in general, so the no-revisit constraint is crucial. Also, discuss using logarithms to convert multiplication to addition, enabling standard shortest-path algorithms with negated weights.
Ask about graph size, possibility of cycles, and whether rates are positive. Confirm that paths cannot revisit currencies and that duplicate directed pairs should use the maximum rate.
Represent currencies as nodes and exchange rates as directed edges with weights equal to the rate (or its logarithm). Deduplicate edges by keeping the maximum rate for each directed pair.
If the graph is a DAG, use topological sort with dynamic programming to find the maximum product path. If cycles are possible, use DFS with backtracking to explore all simple paths, or discuss NP-hardness and potential heuristics.
Code the chosen algorithm, using logarithms to avoid floating-point underflow/overflow and to convert multiplication to addition. Prune paths that cannot beat the current best.
Discuss time and space complexity: DFS is exponential in worst case, while DAG DP is O(V+E). Mention trade-offs between exactness and efficiency, and potential optimizations like memoization if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.