Arbitrage

Time Limit: 1000MS	Memory Limit: 65536K
Total Submissions: 21300	Accepted: 9079

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

——————————————————————————————我是分割線————————————————————————

思路好題。

最短路Bellman-Ford演算法。

用圖中的頂點代表貨幣。

若第i種貨幣能兌換成第j種，匯率為cij，則從頂點i至頂點j連一條有向邊，權值為cij。

問題就轉化成判斷圖中是否存在某個頂點，從它出發的某條迴路上的權值乘積大於1。

大於1即有套匯。

 1 /*
 2     Problem:poj 2240 Arbitrage
 3     OJ:        POJ
 4     User:    S.B.S.
 5     Time:    797 ms
 6     Memory: 856 kb
 7     Length: 1754 b
 8 */
 9 #include<iostream>
10 #include<cstdio>
11 #include<cstring>
12 #include<cmath>
13 #include<algorithm>
14 #include<queue>
15 #include<cstdlib>
16 #include<iomanip>
17 #include<cassert>
18 #include<climits>
19 #include<functional>
20 #include<bitset>
21 #include<vector>
22 #include<list>
23 #include<map>
24 #define F(i,j,k) for(int i=j;i<=k;i++)
25 #define M(a,b) memset(a,b,sizeof(a))
26 #define FF(i,j,k) for(int i=j;i>=k;i--)
27 #define maxn 10001
28 #define inf 0x3f3f3f3f
29 #define maxm 1001
30 #define mod 998244353
31 //#define LOCAL
32 using namespace std;
33 int read(){
34     int x=0,f=1;char ch=getchar();
35     while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
36     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
37     return x*f;
38 }
39 struct EXCHANGE
40 {
41     int ca;
42     int cb;
43     double change;
44 }ex[maxn];
45 char a[maxn],b[maxn];
46 char name[maxn][21];
47 double x;
48 double d[maxn];
49 int ca=0,ans;
50 bool flag=false;
51 int n,m;
52 inline int init()
53 {
54     cin>>n;
55     if(n==0) return 0;
56     for(int i=0;i<n;i++) cin>>name[i];
57     cin>>m;
58     for(int i=0;i<m;i++)
59     {
60         int j,k;
61         cin>>a;cin>>x;cin>>b;
62         for(j=0;strcmp(a,name[j]);j++);
63         for(k=0;strcmp(b,name[k]);k++);
64         ex[i].ca=j;ex[i].change=x;ex[i].cb=k;
65     }
66     return 1;
67 }
68 inline void ford(int u)
69 {
70     flag=false;M(d,0);
71     d[u]=1;
72     F(k,1,n)F(i,0,m-1){
73         if(d[ex[i].ca]*ex[i].change>d[ex[i].cb])
74         {
75             d[ex[i].cb]=d[ex[i].ca]*ex[i].change;
76         }
77     }
78     if(d[u]>1.0) flag=true;
79 }
80 int main()
81 {
82     std::ios::sync_with_stdio(false);//cout<<setiosflags(ios::fixed)<<setprecision(1)<<y;
83     #ifdef LOCAL
84     freopen("data.in","r",stdin);
85     freopen("data.out","w",stdout);
86     #endif
87     while(init()){
88         F(i,0,n-1){
89             ford(i);
90             if(flag) break;
91         }
92         if(flag) cout<<"Case "<<++ca<<": "<<"Yes"<<endl;
93         else cout<<"Case "<<++ca<<": "<<"No"<<endl;
94     }
95     return 0;
96 }

poj 2240