Arbitrage is the use of discrepancies in currency exchange rates to transform one unit of a currency into more than one unit of the same currency. for example, suppose that 1 u. s. dollar buys 49 indian rupees, 1 indian rupee buys 2 japanese yen, and 1 japanese yen buys 0.0107 u. s. dollars. then, by converting currencies, a trader can start with 1 u. s. dollar and buy 49 x 2 x 0.0107 = 1.0486 u. s. dollars, thus turning a profit of 4.86 percent. suppose that we are given n currencies c1, c2, cn and an n x n table r of exchange rates, such that one unit of currency ci buys r[i, j] units of currency cj. a. give an efficient algorithm to determine whether or not there exists a sequence of currencies {ci1, ci2, cik} such that r[i1, i2] * r[i2, i3] r[ik-1, ik] * r[ik, i1] > 1. analyze the running time of your algorithm. b. give an efficient algorithm to print out such a sequence if one exists. analyze the running time of your algorithm.

answer; a coupon clipped from a newpaper,.discounts;

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