hdu 1217 Arbitrage

Arbitrage

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3061 Accepted Submission(s): 1388

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

Recommend

Eddy

题意就是告诉你一些货币之间的汇率。让你判断是否存在一种转换。使得转换会原来的货币后有盈利。

#include <iostream>
#include<map>//map容器建立映射
#include<string>
#include<stdio.h>
using namespace std;

map<string,int> maps;//以string为索引建立映射
double rate[40][40];//记录货币两两之间的转换关系
int n;
int floyd()
{
    int k,i,j;
    for(k=1; k<=n; k++)
        for(i=1; i<=n; i++)
            for(j=1; j<=n; j++)
            {
                if(rate[i][k]*rate[k][j]>rate[i][j])//更新货币间的转换关系
                    rate[i][j]=rate[i][k]*rate[k][j];
                if(i==j&&rate[i][j]>1)//如果通过转换可以盈利
                    return 1;
            }
    return 0;
}
int main()
{
    int id,m,a,b,cases=1;//如题意
    string s1,s2;
    double r;

    while(scanf("%d",&n),n)
    {
        id=1;
        maps.clear();
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
            {
                if(i==j)
                    rate[i][j]=1;
                else
                    rate[i][j]=0;
            }
        for(int i=0; i<n; i++)
        {
            cin>>s1;
            if(!maps[s1])//建立货币和对应标号的映射。数据处理更方便
                maps[s1]=id++;
        }
        cin>>m;
        for(int i=0; i<m; i++)
        {
            cin>>s1>>r>>s2;
            a=maps[s1];
            b=maps[s2];
            rate[a][b]=r;
        }
        printf("Case %d: ",cases++);
        if(floyd())
            printf("Yes\n");
        else
            printf("No\n");
    }
    return 0;
}