poj 1860--Currency Exchange

wshmh

Description




Several currency exchange points are working in our city. Let us suppose that each point specializes in two particular currencies and performs exchange operations only with these currencies. There can be several points specializing in the same pair of currencies. Each point has its own exchange rates, exchange rate of A to B is the quantity of B you get for 1A. Also each exchange point has some commission, the sum you have to pay for your exchange operation. Commission is always collected in source currency.
For example, if you want to exchange 100 US Dollars into Russian Rubles at the exchange point, where the exchange rate is 29.75, and the commission is 0.39 you will get (100 - 0.39) * 29.75 = 2963.3975RUR.
You surely know that there are N different currencies you can deal with in our city. Let us assign unique integer number from 1 to N to each currency. Then each exchange point can be described with 6 numbers: integer A and B - numbers of currencies it exchanges, and real RAB, CAB, RBA and CBA - exchange rates and commissions when exchanging A to B and B to A respectively.
Nick has some money in currency S and wonders if he can somehow, after some exchange operations, increase his capital. Of course, he wants to have his money in currency S in the end. Help him to answer this difficult question. Nick must always have non-negative sum of money while making his operations.


Input




The first line of the input contains four numbers: N - the number of currencies, M - the number of exchange points, S - the number of currency Nick has and V - the quantity of currency units he has. The following M lines contain 6 numbers each - the description of the corresponding exchange point - in specified above order. Numbers are separated by one or more spaces. 1<=S<=N<=100, 1<=M<=100, V is real number, 0<=V<=103.
For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 10-2<=rate<=102, 0<=commission<=102.
Let us call some sequence of the exchange operations simple if no exchange point is used more than once in this sequence. You may assume that ratio of the numeric values of the sums at the end and at the beginning of any simple sequence of the exchange operations will be less than 104.


Output




If Nick can increase his wealth, output YES, in other case output NO to the output file.


Sample Input



3 2 1 20.0
1 2 1.00 1.00 1.00 1.00
2 3 1.10 1.00 1.10 1.00



Sample Output



YES
一个人有s币，问根据所给的兑换方式最后能不能增多- -我们根据货币之间的兑换关系进行建图，
其实最后要问的就是这个图中是不是存在正权回路，一旦出现正权回路，钱币就会不断的增加。
我们知道bellman-ford是用来求最短路径的，同时可以判断是否存在负权回路，那现在只要将其变换成
最长路劲即可- -
我用bellman-ford和spfa都写了一遍，一开始spfa没优化，跑了300+，优化了下跑了16ms差距好大。。


bellman-ford


1 #include<stdio.h>
2 const int MAXN=200;
3 const int INF=-10;
4
5 struct Edge
6 {
7     int u,v;
8     double cost,com;
9 }edge[MAXN];
10
11 int cas;
12 int n,m,s;
13 double dis[MAXN],money;
14
15 void build(int u,int v,double r,double c)
16 {
17     edge[cas].u=u;
18     edge[cas].v=v;
19     edge[cas].cost=r;
20     edge[cas].com=c;
21     cas++;
22 }
23
24 int Bellman_ford()
25 {
26     bool flag;
27
28     int u,v;
29     double c;
30
31     for(int i=0;i<=n;i++)
32     {
33         dis=INF;
34     }
35     dis=money;
36     for(int i=1;i<=n-1;i++)
37     {
38         flag=false;
39         for(int j=0;j<cas;j++)
40         {
41             u=edge[j].u,v=edge[j].v,c=edge[j].com;
42             if(dis[v]<(dis-c)*edge[j].cost)
43             {
44                 dis[v]=(dis-c)*edge[j].cost;
45                 flag=true;
46             }
47         }
48         if(!flag) break;
49     }
50     for(int i=0;i<cas;i++)
51     {
52         u=edge.u,v=edge.v,c=edge.com;
53         if(dis[v]<(dis-c)*edge.cost)
54         {
55             return 1;
56         }
57     }
58     return 0;
59 }
60
61 int main()
62 {
63     int u,v;
64     double a,b,c,d;
65     while(scanf("%d%d%d%lf",&n,&m,&s,&money)!=EOF)
66     {
67         cas=0;
68         for(int i=0;i<m;i++)
69         {
70           scanf("%d%d%lf%lf%lf%lf",&u,&v,&a,&b,&c,&d);
71           build(u,v,a,b);
72           build(v,u,c,d);
73         }
74         if(Bellman_ford()) printf("YES\n");
75         else printf("NO\n");
76     }
77     return 0;
78 }

spfa


1 #include <cstdio>
2 #include <cstring>
3 #include <queue>
4 #include <algorithm>
5 using namespace std;
6 struct cur
7 {
8     int V;
9     double r,c;
10     int next;
11 }map[110*2];
12 int vis[110],first[110*2];
13 double dis[110],v;
14 int n,m,s,cnt;
15 void addedge(int u,int V,double r,double c)
16 {
17     map[cnt].V=V;
18     map[cnt].r=r;
19     map[cnt].c=c;
20     map[cnt].next=first;
21     first=cnt++;
22 }
23 int spfa()
24 {
25     int x,i;
26     deque<int>q;
27     vis=1;
28     dis=v;
29     q.push_back(s);
30     while(!q.empty())
31     {
32         x=q.front();
33         q.pop_front();
34         vis[x]=0;
35         for(i=first[x];i!=-1;i=map.next)
36         {
37             if(dis[map.V]<(dis[x]-map.c)*map.r)
38             {
39                 dis[map.V]=(dis[x]-map.c)*map.r;
40                 if(!vis[map.V])
41                 {
42                     vis[map.V]=1;
43                     if(!q.empty())
44                     {
45                         if(dis[map.V]<dis[q.front()])
46                             q.push_back(map.V);
47                         else
48                             q.push_front(map.V);
49                     }
50                     else
51                         q.push_back(map.V);
52                 }
53             }
54         }
55     }
56     return dis-v>0;
57 }
58 int main()
59 {
60     int a,b,i;
61     double rab,cab,rba,cba;
62     scanf("%d%d%d%lf",&n,&m,&s,&v);
63     cnt=0;
64     memset(first,-1,sizeof(first));
65     for(i=0;i<m;i++)
66     {
67         scanf("%d%d%lf%lf%lf%lf",&a,&b,&rab,&cab,&rba,&cba);
68         addedge(a,b,rab,cab);
69         addedge(b,a,rba,cba);
70     }
71     memset(vis,0,sizeof(vis));
72     memset(dis,0,sizeof(dis));
73     if(spfa())
74         printf("YES\n");
75     else
76         printf("NO\n");
77     return 0;
78 }