This is basically a weighted directed graph problem where you want the max-product path between two nodes.
Model the currencies as nodes in a directed graph where edges are exchange rates, then for each query find the maximum product path from source to target. Use a modified shortest path algorithm (e.g., Bellman-Ford or Dijkstra with max-heap) that maximizes the product of rates, handling negative cycles and unreachable cases.
Pro tip: Mention that exchange rates can be converted to logarithms to turn multiplication into addition, allowing standard shortest path algorithms; but be careful with negative cycles and precision issues.
Represent currencies as nodes and exchange rates as directed edges with weights equal to the rate. For each query, we need the maximum product path from source to target.
Use Bellman-Ford for maximum product paths to handle negative cycles (which correspond to arbitrage opportunities). Alternatively, use Dijkstra with a max-heap if no negative cycles exist, but Bellman-Ford is safer.
If many queries, consider precomputing all-pairs maximum products using Floyd-Warshall (with max and multiplication) or running Bellman-Ford from each source. For q queries, running per query may be acceptable if q is small.
Check for unreachable targets (return -1), and detect positive cycles (arbitrage) that could lead to infinite money. If a positive cycle is reachable and can reach the target, the maximum amount is unbounded (return -1 or special value).
For Bellman-Ford per query: O(n * m) time where n is number of currencies and m is number of rates, and O(n) space. For q queries: O(q * n * m). If using Floyd-Warshall: O(n^3) time and O(n^2) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.