zoj 1092 Arbitrage （poj 2240）

最新推荐文章于 2019-11-01 20:58:31 发布

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最新推荐文章于 2019-11-01 20:58:31 发布

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原文链接：http://www.cnblogs.com/372465774y/archive/2012/11/19/2777589.html

本文介绍了一个程序设计案例，该程序通过输入不同的货币及其兑换率，判断是否存在货币套利机会。通过对给定货币间的兑换率进行计算，判断是否能形成一个转换循环使得最终获得的货币数量超过初始投入。

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Arbitrage

Time Limit: 2 Seconds Memory Limit: 65536 KB

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 Specification

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 c_i of a source currency, a real number r_ij which represents the exchange rate from c_i to c_j and a name c_j 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 Specification


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

//找是否存在大于1的回路
//恶心点在于居然有钱汇同样钱汇率大于1、、不合常理呀
#include <iostream>
#include <stdio.h>
#include <queue>
#include <stack>
#include <set>
#include <vector>
#include <math.h>
#include <string.h>
#include <algorithm>
using namespace std;
char rc[33][22];
double dis[33][33];
char a[22],b[22];
int n,m;
int GetId(char s[])
{
    for(int i=1;i<=n;i++)
    if(strcmp(rc[i],s)==0)
     return i;
}
int main()
{
    int i,j,k;
    int t=1;
    double d;
    while(scanf("%d",&n)==1&&n)
    {
        for(i=1;i<=n;dis[i][i]=1,i++)
         for(j=1;j<=n;j++)
           dis[i][j]=0;
        for(i=1;i<=n;i++)
         scanf("%s",rc[i]);
        scanf("%d",&m);
        while(m--)
        {
           scanf("%s %lf %s",a,&d,b);
            i=GetId(a);
            j=GetId(b);
            dis[i][j]=d;
        }
      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];
      bool f=0;
      for(i=1;i<=n;i++)
        if(dis[i][i]>1)
          {
              f=1;break;
          }
    printf("Case %d: ",t++);
    if(f) printf("Yes\n");else printf("No\n");

    }
    return 0;
}