Shortest path algorithms can be applied in currency trading. let c1 , c2 , . . , cn be various cur- rencies; for instance, c1 might be dollars, c2 pounds, and c3 lire. for any two currencies ci and cj , there is an exchange rate ri, j ; this means that you can purchase ri, j units of currency cj in exchange for one unit of ci . these exchange rates satisfy the condition that ri, j · rj, i < 1, so that if you start with a unit of currency ci , change it into currency cj and then convert back to currency ci , you end up with less than one unit of currency ci (the difference is the cost of the transaction). (a) give an efficient algorithm for the following problem: given a set of exchange rates r i, j , and two currencies s and t, find the most advantageous sequence of currency exchanges for converting currency s into currency t. toward this goal, you should represent the currencies and rates by a graph whose edge lengths are real numbers.