POJ 2240 Arbitrage (Shortest channel), pojarbitrage

POJ 2240 Arbitrage (Shortest channel), pojarbitrage

It gives you the exchange rate relationship between n currencies to determine whether a settlement can be formed. That is, if a currency is changed to another currency multiple times, the result is more than the original one.

The minimum short-circuit of the base is the plus sign for the multiplication number.

#include<cstdio>#include<cstring>#include<string>#include<map>using namespace std;map<string, int> na;const int N = 31;double d[N], rate[N][N], r;int n, m, ans;int bellman(int s){    memset(d, 0, sizeof(d));    d[s] = 1.0;    for(int k = 1; k <= n; ++k)    {        for(int i = 1; i <= n; ++i)        {            for(int j = 1; j <= n; ++j)                if(d[i] < d[j]*rate[j][i])                    d[i] = d[j] * rate[j][i];        }    }    return d[s] > 1.0;}int main(){    int cas = 0;    char s[100], a[100], b[100];    while(scanf("%d", &n), n)    {        na.clear();        ans = 0;        memset(rate, 0, sizeof(rate));        for(int i = 1; i <= n; ++i)        {            rate[i][i] = 1.0;            scanf("%s", s);            na[s] = i;        }        scanf("%d", &m);        for(int i = 1; i <= m; ++i)        {            scanf("%s%lf%s", a, &r, b);            rate[na[a]][na[b]] = r;        }        for(int i = 1; i <= n; ++i)        {            if(bellman(i))            {                ans = 1; break;            }        }        printf("Case %d: %s\n", ++cas, ans ? "Yes" : "No");    }    return 0;}

Arbitrage

Description

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 profit 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 will contain in 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 ci of a source currency, a real number rij which represents the exchange rate from ci to cj and a name cj 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

3USDollarBritishPoundFrenchFranc3USDollar 0.5 BritishPoundBritishPound 10.0 FrenchFrancFrenchFranc 0.21 USDollar3USDollarBritishPoundFrenchFranc6USDollar 0.5 BritishPoundUSDollar 4.9 FrenchFrancBritishPound 10.0 FrenchFrancBritishPound 1.99 USDollarFrenchFranc 0.09 BritishPoundFrenchFranc 0.19 USDollar0

Sample Output

Case 1: YesCase 2: No