NKOJ 1039: Arbitrage
Time Limit: 1500 ms Memory Limit: 10000 kB
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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 US Dollar buys 0.5
British pound, 1 British pound buys 10.0 French francs, and 1 French
franc buys 0.21 US dollar. Then, by converting currencies, a clever
trader can start with 1 US dollar and buy 0.5 * 10.0 * 0.21 = 1.05 US
dollars, making a pro(t of 5 percent.
Your job is to write a program that takes a list of currency exchange
rates as input and then determines whether arbitrage is possible or
not.
Input
The input file will contain one or more test cases. Om the first line of each test case there is an
integer n (1<=n<=30), representing the number of different currencies. The next n lines each
contain the name of one currency. Within a name no spaces will appear. The next line contains one
integer m, representing the length of the table to follow. The last m lines each contain the name c
i
of a source currency, a real number r
ij
which represents the exchange rate from c
i
to c
j
and a name
c
j
of the destination currency. Exchanges which do not appear in the table are impossible.
Test cases are separated from each other by a blank line. Input is terminated by a value of zero (0)
for n.
Output
For each test case, print one line telling whether arbitrage is possible or not in the format "Case
case: Yes" respectively "Case case: No".
Sample Input
3
USDollar
BritishPound
FrenchFranc
3
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