TOJ 1745 Arbitrage floyd-蒲公英云

TOJ 1745 Arbitrage floyd

叁歲伎倆 2022-05-18 02:16 232阅读 0赞

1745: Arbitrage

描述

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.

输入

The input 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.

输出

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

样例输入

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

样例输出

Case 1: Yes
Case 2: No

货币转化问题，先给出n种货币的名称，然后给出m种转化关系，可以以关系建图，问是否可以从转化中获利，用floyd判断一下乘积即可。

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<vector>
using namespace std;
#define inf 0x3f3f3f3f
#define LL long long
int main()
{
    map<string,int>name;
    string s,s2;
    double a[50][50],r;
    int n,m,i,j,k,o=1;
     while(scanf("%d",&n))
    {
        if(n==0)break;
        for(i=1;i<=n;i++)
        {
            cin>>s;
            name[s]=i;
        } 
        for(i=1;i<=n;i++)
           for(j=1;j<=n;j++)
           {
               if(i==j)
               a[i][j]=1;
               else 
               a[i][j]=0;
           } 
        scanf("%d",&m);   
        while(m--)
        {
            cin>>s;
            cin>>r;
            cin>>s2;
            a[name[s]][name[s2]]=r;
        }        
        for(k=1;k<=n;k++)
        {
            for(i=1;i<=n;i++)
            {
                for(j=1;j<=n;j++)
                {
                    if(a[i][j]<a[i][k]*a[k][j])
                    {
                        a[i][j]=a[i][k]*a[k][j];
                    }
                }
            }
        }    
        bool flag=false;
        for(i=1;i<=n;i++)
        {
            if(a[i][i]>1)
              {
                flag=true;
                break;
              }
        }
        if(flag)  
        printf("Case %d: Yes\n",o++);
        else 
        printf("Case %d: No\n",o++);      
    }
}