Currency Exchange

Time Limit: 1000MS   Memory Limit: 30000K
Total Submissions: 35610   Accepted: 13646

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

Source

Northeastern Europe 2001, Northern Subregion

 

               有n种货币，m个交换所，每个交换所中只能交换两种货币，货币交换分别需要汇率和固定税款（可能是）来看，交易中的货币公式  （now-c（税款））*r（汇率）；

                这道题呢，千万不要把m当作点，而应将n中货币当作点，然后把商店的兑换当作路径，其中以往用作计算距离的数组d在这里意义是在之前你所掌握的一次性最多的这种货币数额为多少，这样的话，就相当于是个跑一个spfa判断有无负环就是了；

 

#include<iostream>
#include<cstdio>
#include<queue>
using namespace std;
int head[105];
struct ***
{
	int to, ne;
	double r,c;
}ed[1000005];
int time[105];
int vis[105];
int cnt, n, m, tn;
double tsum;
void add(int from, int to, double r,double c)
{
	ed[cnt].to = to;
	ed[cnt].r = r;
	ed[cnt].c = c;
	ed[cnt].ne = head[from];
	head[from] = cnt++;
}
double d[105];
void init()
{
	for (int s = 1; s <= n; s++)
	{
		time[s] = 0;
		head[s] = -1;
		d[s] = 0;
		vis[s] = 0;
	}
	cnt = 0;
}

void spfa()
{
	queue<int>q;
	q.push(tn);
	d[tn] = tsum;
	vis[tn] = 1;
	while (!q.empty())
	{
		int t = q.front();
		q.pop();
		vis[t] = 0;
		for (int s = head[t]; ~s; s=ed[s].ne)
		{
			if (d[ed[s].to] < (d[t] - ed[s].c)*ed[s].r)
			{
				d[ed[s].to] = (d[t] - ed[s].c)*ed[s].r;
				if (!vis[ed[s].to])
				{
					time[ed[s].to]++;
					q.push(ed[s].to);
					vis[ed[s].to] = 1;
				}
				if (time[ed[s].to] > n)
				{
					printf("YES\n");
					return;
				}
			}
		}
	}
	printf("NO\n");
}
int main()
{
	while (~scanf("%d%d%d%lf", &n, &m, &tn, &tsum))
	{
		init();
		while (m--)
		{
			int a, b;
			double rab, cab, rba, cba;
			scanf("%d%d%lf%lf%lf%lf", &a, &b, &rab, &cab, &rba, &cba);
			add(a, b, rab, cab);
			add(b, a, rba, cba);
		}
		spfa();
	}
}