Currency Conversion: Weighted-Graph Path Product

A Rippling interviewer hands you a handful of exchange rates and asks for conversions that are not on the list. You might be told what a dollar is worth in euros and what a euro is worth in yen. Then you get asked for dollars to yen, or yen back to dollars, or a pair with no connection at all. The rates you are given are single steps between neighbors, and each query wants the whole chain that links two currencies the list never connects directly.

Every rate is a directed edge in a small graph. A currency is a node, and a rate from one currency to another is an edge whose weight is the conversion factor. Give each edge a twin running the other way at the reciprocal weight, since a dollar worth two euros means a euro is worth half a dollar. A conversion is then a walk from the start node to the target, and the answer is the product of the weights along the way. If no walk exists, or either currency was never mentioned, the answer is -1.