Currency Exchange
| Time Limit: 1000MS | Memory Limit: 30000K | |
| Total Submissions: 16635 | Accepted: 5821 |
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.
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.
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
bellman-ford算法，题目大意是有N种货币和M个货币交换点，Nick有一些其中一种货币，每两种货币兑换有一个公式，就是（本金 - 手续费) * 转换率，每个交换点只能交换某两种特定的货币，最后问是否可以通过这些交换点使得最后的本金会增加
bellman-ford计算是否有负圈回路就好，其实就是判断是否有使本金增长的圈
#include<stdio.h>
double map[101][101][2];
double dis[101];
int n, m, s;
double v;
bool bellman()
{
int i, j, k;
for(i = 1; i < 101; i++)
{
dis[i] = 0;
}
dis[s] = v;
for(i = 1; i < n; i++)
{
for(j = 1; j <= n; j++)
{
for(k = 1; k <= n; k++)
{
if(map[j][k][0] > 0)
{
if(dis[k] < (dis[j] - map[j][k][1]) * map[j][k][0])
{
dis[k] = (dis[j] - map[j][k][1]) * map[j][k][0];
}
}
}
}
}
for(j = 1; j <= n; j ++)
{
for(k = 1; k <= n; k++)
{
if(dis[k] < (dis[j] - map[j][k][1]) * map[j][k][0])
return 0;
}
}
return 1;
}
int main()
{ scanf("%d %d %d %lf", &n, &m, &s, &v);
int i = m;
int a, b;
while(i--)
{
scanf("%d %d", &a, &b);
scanf("%lf %lf %lf %lf", &map[a][b][0], &map[a][b][1], &map[b][a][0], &map[b][a][1]);
}
if(bellman() == 0)
printf("YES\n");
else
printf("NO\n");
return 0;
}