Algorithm not code

Arbitrage is the use of discrepancies in currency-exchange rates to make a profit. For

example, there may be a small window of time during which 1 U.S. dollar buys 0.75 British pounds,

1 British pound buys 2 Australian dollars, and 1 Australian dollar buys 0.70 U.S. dollars. At such a

time, a smart trader can trade one U.S. dollar and end up with 0:75 2 0:7 = 1:05 U.S. dollarsa

profit of 5%. Suppose that there are n currencies c1; : : : ; cn and an n n table R of exchange rates,

such that one unit of currency ci buys R[i; j] units of currency cj . Devise and analyze an algorithm to

determine the maximum value of R[c1; ci1]R[ci1; ci2]R[cik1; cik]R[cik; c1]