ACM HDU 1217 Arbitrage(Floyed算法）

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本文介绍了一种使用图算法来检测货币交易中是否存在套利机会的方法。通过输入各种货币之间的兑换率，该算法能够判断是否可以通过一系列转换使初始货币数量增加，即是否存在套利空间。

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Arbitrage

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1186 Accepted Submission(s): 547

Problem 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 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.

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 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
  

Sample Output

   Case 1: Yes Case 2: No
  

Source

University of Ulm Local Contest 1996

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#include<stdio.h>
#include<iostream>
#include<map>
using namespace std;
map<string,int>name;
#define MAXN 30
double g[MAXN][MAXN];
//*****************************************************
//Floyed算法,求任意两个顶点间的最短路径
//dis[][]记录任意两点间的最短路径，初始的dis[][]记录直接路径 
//*****************************************************
#define typec double
void floyed(typec dis[][MAXN],int n)//节点从1~n编号
{
int i,j,k;
for(k=1;k<=n;k++)
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(dis[i][j]<dis[i][k]*dis[k][j])
                 dis[i][j]=dis[i][k]*dis[k][j];

}     
//**********************************************************
int main()
{
int n,i,m,j;
string str1,str2;
double r;
int iCase=0;
while(scanf("%d",&n),n)
    {
        iCase++;
for(i=1;i<=n;i++)
        {
            cin>>str1;
            name[str1]=i;
        }
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
           {
if(i==j)g[i][j]=1;
else g[i][j]=0;
           }    
        scanf("%d",&m);   
while(m--)
        {
            cin>>str1>>r>>str2;
            g[name[str1]][name[str2]]=r;
        }     
        floyed(g,n);
bool flag=false;
for(i=1;i<=n;i++)
if(g[i][i]>1)
          {flag=true;break;}
if(flag)  printf("Case %d: Yes\n",iCase);
else printf("Case %d: No\n",iCase);
    }    
return 0;
}