hdu 1217(Floyed)

Arbitrage

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6522    Accepted Submission(s): 3019

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

 

题意：n种货币，有m种汇率,问某种货币能否通过汇率交易之后变得更多？

题解：假设某种货币最初是1,然后寻找某条回路，看最后它能不能变得比1更大,用Floyed就可以更新出所有的结果.

import java.util.HashMap;
import java.util.Scanner;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = ;
        while(sc.hasNext()){
            int n = sc.nextInt();
            if(n==) break;
            double [][] map = new double [n][n];
            HashMap<String,Integer> hm = new HashMap<String,Integer>();
            for(int i=;i<n;i++){
                String str = sc.next();
                hm.put(str,i);
            }
            int m = sc.nextInt();
            while(m-->){
                String str1 = sc.next();
                double v = sc.nextDouble();
                String str2 = sc.next();
                int a = hm.get(str1);
                int b = hm.get(str2);
                map[a][b]= v;
            }
            for(int k=;k<n;k++){
                for(int i=;i<n;i++){
                    for(int j=;j<n;j++){
                        if(map[i][j]<map[i][k]*map[k][j]) map[i][j] = map[i][k]*map[k][j];
                    }
                }
            }
            boolean flag = false;
            for(int i=;i<n;i++) if(map[i][i]>){flag=true;break;}
            System.out.print("Case "+(t++)+": ");
            if(flag) System.out.println("Yes");
            else System.out.println("No");
        }
    }
}