Arbitrage
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 10997 | Accepted: 4622 |
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 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
其实题目的大意就是能不能通过各个国家汇率的不同赚到比当初更多的钱。
也就是spfa判环
#include <stdio.h>
#include <vector>
#include <string.h>
#include <queue>
using namespace std;
int n,m;
//邻接表
vector<int>map[33];
//存贮国家名字
char name[33][100];
//两个国家的汇率
double f[33][33];
//起点国家到当前国家转换后的货币量
double price[33];
//入度
int in_degree[33];
//进队列的次数
int sum[33];
//是否在队列
bool in_queue[33];
int tonum(char *str)
{
for(int i=0;i<n;i++)
if(strcmp(str,name[i])==0)
return i;
}
bool spfa(int x)
{
queue<int>s;
sum[x]++;
price[x]=1.0;
in_queue[x]=true;
s.push(x);
while(!s.empty())
{
int pos=s.front();
s.pop();
in_queue[pos]=false;
for(int i=0;i<map[pos].size();i++)
{
int edge=map[pos][i];
if(price[edge]<price[pos]*f[pos][edge])
{
price[edge]=price[pos]*f[pos][edge];
if(!in_queue[edge])
{
in_queue[edge]=true;
s.push(edge);
if(++sum[edge]>in_degree[edge])
{
return true;
}
}
}
}
}
return false;
}
int main()
{
int t=0;
while(~scanf("%d",&n))
{
if(n==0)
break;
memset(in_degree,0,sizeof(in_degree));
memset(name,0,sizeof(name));
memset(map,0,sizeof(map));
memset(f,0,sizeof(f));
for(int i=0;i<n;i++)
scanf("%s",name[i]);
scanf("%d",&m);
for(int i=0;i<m;i++)
{
char str1[100],str2[100];
memset(str1,0,sizeof(str1));
memset(str2,0,sizeof(str2));
double x;
scanf("%s %lf %s",str1,&x,str2);
int a=tonum(str1);
int b=tonum(str2);
f[a][b]=x;
in_degree[b]++;
map[a].push_back(b);
}
bool ok=false;
for(int i=0;i<n;i++)
{
if(spfa(i))
{
ok=true;
break;
}
memset(in_queue,false,sizeof(in_queue));
memset(price,0,sizeof(price));
memset(sum,0,sizeof(sum));
}
if(ok)
printf("Case %d: Yes\n",++t);
else
printf("Case %d: No\n",++t);
}
return 0;
}