POJ 2240:Arbitrage

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本文介绍了一种使用弗洛伊德算法检测货币套利可能性的方法。通过构建货币兑换率图，算法能判断是否存在从一种货币开始，经过一系列兑换后，最终获得超过初始金额的情况，即是否存在套利机会。

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2240:Arbitrage

总时间限制:

1000ms

内存限制:

65536kB

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

0

样例输出

Case 1: Yes
Case 2: No

来源

Ulm Local 1996

题解：floyd直接过，需要注意的是，因为名称是字符串所以需要map或者自己映射一下，下面是AC代码：

#include"iostream"
#include"string"
#include"map"
#include"cstring"

using namespace std;

double jz[32][32]={0.0};
int n;
int m,p=1;

int floyd()
{
	for(int k=1;k<=n;k++)
		for(int i=1;i<=n;i++)
			for(int j=1;j<=n;j++)
			{
				if(jz[i][j]<jz[i][k]*jz[k][j])
					jz[i][j]=jz[i][k]*jz[k][j];
				if(jz[1][1]>1) return 1;//当美元到美元的转换大于的时候就可以转换
			}
	return 0;
}
int main()
{
	while(cin >> n)
	{
		memset(jz,0,sizeof(jz));
		if(n == 0) break;
		map<string,int> mp;
		for(int i=1;i<=n;i++)
		{
			string s;
			cin >> s;
			mp[s]=i;
		}
		cin >> m;
		for(int i=1;i<=m;i++)
		{
			string s,s2;
			double money;
			cin >> s >> money >> s2;
			jz[mp[s]][mp[s2]]=money;
		}
		if(floyd())
			cout << "Case " << p++ << ": Yes" << endl;
		else 
			cout << "Case " << p++ << ": No" << endl;
		
	}
	return 0;
}