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.

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 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. 

For each test case, print one line telling whether arbitrage is possible or not in the format "Case case: Yes" respectively "Case case: No". 

3
USDollar
BritishPound
FrenchFranc
3
USDollar 0.5 BritishPound
BritishPound 10.0 FrenchFranc
FrenchFranc 0.21 USDollar

3
USDollar
BritishPound
FrenchFranc
6
USDollar 0.5 BritishPound
USDollar 4.9 FrenchFranc
BritishPound 10.0 FrenchFranc
BritishPound 1.99 USDollar
FrenchFranc 0.09 BritishPound
FrenchFranc 0.19 USDollar

0

Case 1: Yes
Case 2: No

University of Ulm Local Contest 1996

原题链接： http://acm.hdu.edu.cn/showproblem.php?pid=1217

给了你集中货币，及其之间的汇率，问你是否存在某种货币经过与其他货币的进行一个回路的兑换后能否获利。

#include <iostream>
#include <cstdio>
#include <map>
#include <queue>
using namespace std;
double a[35][35];
double dis[35];
bool vis[35];
int n;

bool spfa(int s)
{
    for(int i=1;i<=n;i++)
    {
        dis[i]=0;
        vis[i]=false;
    }
    dis[s]=1.0;
    vis[s]=true;
    queue<int>q;
    q.push(s);
    while(!q.empty())
    {
        int p=q.front();
        q.pop();
        vis[p]=false;
        for(int i=1;i<=n;i++)
        {
            if(dis[i]<dis[p]*a[p][i])
            {
                dis[i]=dis[p]*a[p][i];
                if(!vis[i])
                {
                    vis[i]=true;
                    q.push(i);
                }
                if(dis[s]>1.0)
                    return true;
            }
        }
    }
    return false;
}

int main()
{
    int kase=0;
    map<string,double>mapp;
    char s1[35],s2[35];
    while(cin>>n,n)
    {
        mapp.clear();
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
                if(i==j) a[i][j]=1.0;
                else a[i][j]=0;
        }
        for(int i=1; i<=n; i++)
        {
            scanf("%s",s1);
            mapp[s1]=i;
        }
        int t;
        cin>>t;
        double d;
        while(t--)
        {
            scanf("%s%lf%s",s1,&d,s2);
                int x=mapp[s1];
                int y=mapp[s2];
                a[x][y]=d;
        }
        cout<<"Case "<<++kase<<": ";
        bool flag=true;;
        for(int i=1;i<=n;i++)
        {
            if(spfa(i))
            {
                flag=false;
                cout<<"Yes"<<endl;
                break;
            }
        }
        if(flag)
            cout<<"No"<<endl;
    }
    return 0;
}