7. The risk-free currency exchange problem offers a risk-free way to make money. Suppose we have currencies Ci,...,cn (For example, ci might be dollars, c2 rubles, cs yen, etc.) For every two currencies ci and cj there is an exchange rate rij such that you can exchange one unit of ci for rij units ofcj. Note that ifmj .rji > 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 ch ,ch, , cu such that rive . rias . . . . r4-1,4 . rk,il 1, then trading one Fiss>, then trading one unit of ci into ci and trading that into ci, 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.) 7. The risk-free currency exchange problem offers a risk-free way to make money. Suppose we have currencies Ci,...,cn (For example, ci might be dollars, c2 rubles, cs yen, etc.) For every two currencies ci and cj there is an exchange rate rij such that you can exchange one unit of ci for rij units ofcj. Note that ifmj .rji > 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 ch ,ch, , cu such that rive . rias . . . . r4-1,4 . rk,il 1, then trading one Fiss>, then trading one unit of ci into ci and trading that into ci, 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.)