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HDU1217 Arbitrage 【SPFA】

2024-07-17 04:11:26   222人阅读

Arbitrage

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4460    Accepted Submission(s): 2032


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 
题意：给定各个货币间的汇率，问存不存在套现环。

题解：这题类似于找负环，所以用SPFA。

#include <stdio.h>
#include <string.h>
#include <string>
#include <queue>
#include <map>
#define maxn 36
using namespace std;

double rate[maxn][maxn], dist[maxn];
bool vis[maxn];

void SPFA(int s, int n)
{
	int i, j, now, tmp;
	for(i = 1; i <= n; ++i){
		vis[i] = 0; dist[i] = 0.0;
	}
	queue<int> Q;
	dist[s] = 1.0; vis[s] = 1;
	Q.push(s);
	while(!Q.empty()){
		now = Q.front(); Q.pop();
		vis[now] = 0;
		for(i = 1; i <= n; ++i){
			if(dist[i] < dist[now] * rate[now][i]){
				if(!vis[i]) Q.push(i); vis[i] = 1;
				dist[i] = dist[now] * rate[now][i];
				if(dist[s] > 1) return;
			}
		}
	}
}

int main()
{
	int n, i, m, cas = 1;
	char buf[50], buf2[50];
	double val;
	map<string, int> mp;
	while(scanf("%d", &n), n){
		mp.clear();
		memset(rate, 0, sizeof(rate));
		for(i = 1; i <= n; ++i){
			scanf("%s", buf);
			mp[buf] = i;
		}
		scanf("%d", &m);
		for(i = 0; i < m; ++i){
			scanf("%s%lf%s", buf, &val, buf2);
			rate[mp[buf]][mp[buf2]] = val;
		}
		SPFA(1, n);
		printf("Case %d: %s\n", cas++, dist[1] > 1 ? "Yes" : "No");
	}
	return 0;
}


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