The risk-free currency exchange problem offers a risk-free way to make money. suppose we have currencies cn. (for example, c1 might be dollars, c2 rubles, c3 yen, etc.) for every two currencies ci and cj there is an exchange rate ri, j such that you can exchange one unit of ci for ri, j units of cj . note that if ri, j ·rj, i > 1, then you can make money simply by trading units of currency i into units of currency j and back again. this almost never happens, but occasionally (because the updates for exchange rates do not happen quickly enough) for very short periods of time exchange traders can find a sequence of trades that can make risk-free money. that is, if there is a sequence of currencies ci1 , ci2 cik such that ri1,i2 ·ri2,i3 ·rik−1,ik ·rik, i1 > 1, then trading one unit of ci1 into ci2 and trading that into ci3 and so on will yield a profit. design an efficient algorithm to detect if a risk-free currency exchange exists. (you need not actually find it.)